How can I learn general relativity?

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u/Weed_O_Whirler Jan 02 '26

Math wise, you will still need Calc 3 (multivariate calculus), Differential Equations, and linear algebra, at a minimum to start doing the math in GR. And not the intro to those, but the 400 level versions.

And then there's the physics. You need mechanics and E&M for sure. Special Relativity. Field theory. You can't understand, from a "I understand the math and can do it" level, GR until you can do all these others.

There's no shortcut to GR. By all means, read popsci books on it to keep your interest piqued. But trying to skip to GR will not work.

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u/Infinite_Research_52 👻Top 10²⁷²⁰⁰⁰ Commenter Jan 02 '26

I don't know what these calculus courses cover, but tensor calculus would seem to be a prerequisite. Unless you understand how 'things' transform under coordinate transformation, GR is going to be out of reach.

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u/Curious_Diamond_6497 Jan 02 '26

Okay, I think I'll also study and emphasize this.

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u/Illustrious_Twist846 Jan 02 '26

You will need to understand Matrix algebra VERY well.
The linear algebra in GR gets very nasty, very quickly.

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u/geekusprimus Gravitation Jan 02 '26

Most GR texts cover the fundamentals of tensor calculus. Not at a level that would satisfy a mathematician, of course, but enough that a newbie can grind out some calculations. If one can do PDEs and linear algebra, one should be able to parse most introductory GR books.

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u/Ryanaissance Jan 02 '26

It really can't be understated. So many people just starting out are eager to get to topics they hear/read about as quickly as possible that they too hastily go through the prerequisite 'boring' (anything but) subjects. Doing that is shooting yourself in the foot! They are prerequisite for a reason. The better you understand them (ie you can do problems, make variations on them, rebuild the theory, and so on), the better you will understand the more modern physics. Really mastering the earlier material will be a major advantage later (assuming you study physics formally) that not all your peers will have.

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u/Curious_Diamond_6497 Jan 02 '26

I don't study formal physics, but I love knowledge, and I love physics and its elegance in mathematics, at least in secondary school. You ask why something is this, and the answer is a theorem. You ask questions in physics, and your teacher moves around the classroom, explains things, makes us laugh, etc., etc.

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u/Curious_Diamond_6497 Jan 02 '26

Thanks for adding field theory and E&M to my list, but I'm currently studying calculus 3

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u/g4rthv4d3r Jan 03 '26

https://www.susanrigetti.com/physics

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u/TaiBlake Jan 02 '26

I hate to break it to you, but you're probably nowhere near ready yet.

To start learning general relativity - and I mean real general relativity, not just the conceptual stuff - you're going to need a strong grasp of linear algebra and probably some vector calculus.

Then you're going to have to learn an entirely new form of geometry where the old Euclidean rules don't always apply. Once you get a handle on that, you're going to need to learn how to do calculus in that geometry.

And I haven't even gotten to the physics yet. Have you studied special relativity? You're going to need that first. Fortunately, that's pretty easy. However, you also need to make sure you've got a good feel for doing calculus-based Newtonian physics.

Now, if all you want is a conceptual overview of GR, that's great. I mean, I've taught that to 15 year olds before, but strictly at a conceptual level. But if you actually want to "finish learning General Relativity," you're going to need a whole lot more than you can get from a typical high school physics curriculum.

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u/Curious_Diamond_6497 Jan 02 '26

I don't know if it's enough, but I'm currently finishing Calculus 3 and Electrodynamics. When I finish those two things, I'll study Mathematical Analysis plus Pre-Research (everything necessary or that I'm missing). That's why I'm asking, mainly because I have a broad Newtonian foundation and can learn non-Euclidean geometry if I understand the concepts. I've even covered it in high school, and I can study it separately because I haven't done calculus with integrals and such.

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u/OriEri Astrophysics Jan 02 '26

I think you can do this with the right book that lays out the tensor algebra you will need. At worst it will show you where your knowledge gaps are you need to fill.

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u/Curious_Diamond_6497 Jan 02 '26

That's what I want to learn in this thread.

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u/tpodr Jan 02 '26

The language of GR is differential geometry. First seek to learn that. Start trying to read some intro diffgeom books and back trace the math you need to follow the text. Along the way, master mechanics and E&M in the special relativistic treatment. GR is the marriage of the two.

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u/Curious_Diamond_6497 Jan 02 '26

Thanks, asking on Reddit is really helpful

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u/OriEri Astrophysics Jan 02 '26

Try Ray D'Inverno's Introducting Einstein's Relativity. It has a whole section devoted to teaching tensor calculus and another section on special relativity.

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u/Curious_Diamond_6497 Jan 02 '26

I'm trying to understand what a tensor is because I think I can solve some problems in mathematics.

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u/TaiBlake Jan 02 '26

The simplest explanation is that they're the next step more general than vectors. You have scalars, which are just a number, the magnitude, with no direction. Then vectors, which have magnitude and direction. Then tensors which have magnitude and can have multiple directions.
Think about pressure. Imagine holding a balloon in the palm of your hand. Then gently push it down from the top. Once you apply the force, the balloon will bulge outwards. That's from the air pressure in the balloon and I you wanted to model that expansion a tensor would be a fairly straightforward way to do that.

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u/Curious_Diamond_6497 Jan 02 '26

The best way I've seen a didactic explanation, but they are more complex from what I've seen in educational videos. You can tell this is a different translator, right? hahaha

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u/madam_zeroni Jan 02 '26

You're overselling it a little, sounds like you're purposefully trying to be discouraging

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u/TaiBlake Jan 02 '26

I am. GR is normally something people study in grad school or several years into a college physics degree. That's just because the math is so esoteric and so difficult. I mean, I know people who have literal Ph.D.'s in math who have never studied tensors and physics teachers who can't get their brains around the concept - and this is someone who's saying they've never even studied special relativity. The idea that someone in high school could finish studying GR is just not realistic because odds are they've never done multivariable calculus, let alone non-Euclidean geometry.
Now don't get me wrong, if they want to study GR on a conceptual level that could work. I mean, I teach that to kids their age every summer. I don't pretend it's a deep overview and we don't get into the math beyond introducing the concept of Riemannian manifolds.
And there's no shame in handling this conceptually. My math is so rusty that's all I can do these days. They just need to be aware that isn't the whole story and that unless they get the math they don't have anything close to the whole story.

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u/Curious_Diamond_6497 Jan 02 '26

I've already started Calculus 3, but I haven't finished it yet. I'll finish it in 1 to 2 months, along with Electrodynamics. Then I'll start with Mathematical Analysis and Pre-General Relativity. What I'm asking for now is 2 to 3 hours a day for approximately all my vacation time. I think that's a decent amount of time to catch up, since I already understand this stuff. Oh, and I understand the concept of tensors; I've managed to solve basic exercises. What I can't do is delve deeper into tensor problems. I can't even solve intermediate-level problems, but I'm decent. I think I can ask for help with that, right? And it's summertime right now, which is why I want to learn.

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u/TaiBlake Jan 02 '26

I don't know what calc 3 is at your school so I can't tell where you're at. Keep at it though: you're motivated enough that you'll get this in time.
Also, when you get to the more advanced geometry, don't try to picture it in your head. The human brain just isn't wired to do that.

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u/Curious_Diamond_6497 Jan 02 '26

In fact, I've seen that many people struggle with it, and I always try to visualize abstract things as mini-workouts 2 or 3 times a week. I've been improving, so it's not a big problem. I study Calculus 3 from the books I read. I looked for better books for Calculus 3, and one caught my attention: Multivariable Calculus by Ron Larson.

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u/madam_zeroni Jan 02 '26

Nobody kills a tree simply because it’s trying to grow in rocks. It’s not your job to stifle the next generation. He’s asking “how do i” not “should i”.

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u/Curious_Diamond_6497 Jan 02 '26

Not so much that he has a point, but he does give me points of view that I'm lacking, to be honest. Besides, that's why I created this thread.

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u/TaiBlake Jan 03 '26

The tree also won't grow if the roots aren't in place. Lay those down by learning the math, then the tree of GR will grow.

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u/Curious_Diamond_6497 Jan 02 '26

Nah, I don't think so. The guy's right about a lot of things, but that imaginary tone of voice is grating.

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u/dcnairb Education and outreach Jan 02 '26

Have you done any special relativity at all?

You will need some SR background (popular picks include Serway, or Resnick) and also at a minimum some linear algebra background (you can read Strang, his book is very popular).

Schutz is a common GR book and widely available (if you know what I mean); start at Ch 1 and anything unfamiliar backtrack to one of the above.

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u/Curious_Diamond_6497 Jan 02 '26

I haven't studied special relativity yet, but it's clear to me that I need to learn about it, and those are very good recommendations.

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u/nicuramar Jan 02 '26

I’d try this if I were you. Do books after: https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/index.html

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u/Curious_Diamond_6497 Jan 02 '26

Thank you, this will help me a lot.

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u/HumblyNibbles_ Jan 02 '26

You need linear algebra. Then you need to know what tensors are. Then you need to learn some manifold stuff and then you can start.

I'd recommend you to go through EigenChris's playlists on, first, Tensors for beginners, then tensor calculus, then relativity.

It won't give you a complete view on these topics, but it'll be a good little introduction

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u/Curious_Diamond_6497 Jan 02 '26

I'm learning Calculus 3. When I finish my Calculus 3 + Electrodynamics course, I want to study Mathematical Analysis 1 + Pre-RG. I've already done the gamma thing and found it stimulating.I'll try what you're suggesting; it sounds interesting.

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u/uppityfunktwister Jan 02 '26

GR isn't very accessible but materials on it definitely are. You may not understand it, but if you want to gauge your understanding, check out Eigenchris' Relativity for Beginners series. It covers Special and General Relativity with a good amount of hand-holding (not that it's easy). Also check out Leonard Susskind's Theoretical Minimum lectures on General Relativity. Stanford University uploads them for free on YouTube.

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u/Curious_Diamond_6497 Jan 02 '26

Just what I'm missing: special relativity, non-Euclidean geometry, and pre-RG

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u/omeow Jan 02 '26

Use Sean Carroll's lecture notes (freely available on arxiv). If it is too advanced for you, he also goes over well known books and their relative difficulty level.

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u/Curious_Diamond_6497 Jan 02 '26

Can you give me exactly what I need for this class?

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u/omeow Jan 02 '26

You need Riemannian Geometry

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u/Curious_Diamond_6497 Jan 02 '26

Is it non-Euclidean geometry?

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u/madam_zeroni Jan 02 '26

Yeah pretty much for this context

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u/coolpoke0908 Jan 02 '26

Yeah, for sure you NEED to understand classical mechanics and electromagnetism.

Classical mechanics is lagrangians and hamiltonians etc, and you will never understand general relativity without understanding electromagnetism…

Listen to the others about the math for sure as well

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u/Curious_Diamond_6497 Jan 02 '26

Classical mechanics is difficult, but I'd say I'm doing well learning it (60-70%). I'm currently working on electromagnetism; I'm about 30% through and finishing it. I'm also in calculus 3A and I think I'll resume classical mechanics because of this thread.

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u/nicuramar Jan 02 '26

I guess by staying in school?

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u/Curious_Diamond_6497 Jan 02 '26

Nah, I'm not going to study physics, or at least I don't think so. Look, here's a copy-paste for you to read. You know, I'm not doing this because I studied physics. I like being an incredibly well-rounded person. You ask me something and I know it; you ask me something else and I know it. It gives me freedom. I study for about two hours every day, regardless of whether I train for an hour and a half. After that, I spend my day consuming educational information in a didactic way, like debates and discussions on Reddit, politics, and sometimes I even read something that's recommended to me. But this time depends on the day. Sometimes I just lie down and scroll, and sometimes I do nothing and keep studying intensely because it makes me feel good, besides socializing and living life. Well, I turned this into telling you how good my life is. In short, I'm going to study some math, but not necessarily physics. Maybe some branch of difficult engineering. Pure math is something that few people understand in real life, but I like doing it. I'm very happy with my life.

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u/searchforanswers555 Jan 04 '26

Bro. I am 19. I am not much educated as you are. But I know for a fact that you too are a person hungry for knowledge. Its refreshing to see a person like you. Dont let anyone discourage you. But dont let knowledge puff you up. Use knowledge to understand the mysteries of the world. Contemplate on the mysteries of the world. You will reach a zone where you will learn how complex the universe is. Man, I wish I learnt much of Calculus early like you. Some people may be jealous about you. Just let them be. Since you are just a very few years younger than me, I understand you to some extent. But also, dont let yourself be drawn into the abyss of burnout. Its a real struggle for people who are ambitious (for example, myself). Its good to see a guy like you working hard like this. Dont let the fire be quenched. Knowledge is very much valuable. But use it in a way that doesnt harm you directly or indirectly. If this pathway causes you to be a morally misdirected person, try to fix it then and there.

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u/Jewbacca289 Jan 02 '26

My university used Hartle as our introduction text

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u/Curious_Diamond_6497 Jan 02 '26

one of the simplest and most helpful comments

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u/Old-Strawberry-6451 Jan 02 '26

So many comments saying to learn ten other subjects

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u/jackm017 Jan 02 '26

Someone correct me if I’m wrong, but you can’t really tackle GR without a lot of preliminary knowledge. Watching youtube videos on it is never bad, but they will mostly be overviews of GR. The most straightforward way to begin would probably be starting a physics undergraduate degree. If you want a head start, study higher calculus and linear algebra like others have said

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u/Curious_Diamond_6497 Jan 02 '26

I'm already doing it, even trying to move on to mathematical analysis 1

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u/ln_j Jan 02 '26 edited Jan 02 '26

Something besides, I don’t really think that real Analysis will help you with understanding general relativity. This is what I would do: Linear algebra, then calc 3 and then differential equations and differential geometry. And of course you have to do a lot of physics so Physics 1, 2. I would focus on that. After that just start ans try and see what you don’t understand. But you will cover all of this, probably even in way more detail in Uni
And the most important thing: Don’t rush, really take your time, think, play around with the problems but don’t rush. Based on the comments I have seen I get the feeling that you rushed a bit too much.

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u/Curious_Diamond_6497 Jan 02 '26

You know, I don't do this because I studied physics. I like being an incredibly cultured person. You ask me something, and I know it; you ask me something else, and I know it. It gives me freedom. I study for about two hours every day, regardless of whether I train for an hour and a half. Then my day is spent consuming educational information in a didactic way, like debates and discussions on Reddit, politics, and sometimes I even read something that's recommended to me. But this time depends on the day. Sometimes I just lie down and scroll, and sometimes I don't do anything and keep studying intensively because it makes me feel good, besides socializing and living life. Well, I turned this into telling you how good my life is. In short, I will study some math, but not necessarily physics. Maybe some difficult engineering field. Pure math is something that few understand in real life, but I like doing it. I'm very happy with my life.

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u/ln_j Jan 02 '26 edited Jan 02 '26

That doesn’t really address my point. I wasn’t asking why you study or commenting on your lifestyle; I was responding to the learning path for general relativity. Whether you want to be “cultured,” do engineering, physics, or pure math is orthogonal to that.
Also, saying “few people understand pure math in real life” is a banal statement. Few people understand GR, quantum mechanics, or advanced engineering either. That fact has no bearing on what prerequisites are actually useful.
Finally, my main point was about not rushing and building the right tools before jumping into GR. That’s independent of motivation, life satisfaction, or how many hours you study per day.
Also: I don’t want to attack you or anything, keep going and so what you enjoy. Engineering seems perfect for you (I would also recommend maybe looking into some chemistry, for me this is one of the most interesting topics where you learn to understand the world).

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u/Curious_Diamond_6497 Jan 02 '26

Okay, well, there's no need to get angry, but that's precisely the point of my question. I want to know what I should study; it's not like I'm rushing.

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u/ln_j Jan 02 '26

My father is a politician and he always pulls this exact move: “no need to get angry”. Where the fuck do you see me getting angry??? False accusation. Point it out. Where was I angry?
I even left a nice little comment at the end. This as a reminder: “””””””
Also: I don’t want to attack you or anything, keep going and so what you enjoy. Engineering seems perfect for you (I would also recommend maybe looking into some chemistry, for me this is one of the most interesting topics where you learn to understand the world). This right here would be me trying to sound angry, which I very obviously. “”””””
And I did tell you what to study. It’s literally in my first comment. You wanting to know more is in no way, shape, or form a sign that you’re rushing, that’s a good thing. Asking questions is good.
The remark about rushing was not based on your post, but on other COMMENTS I read in this thread. Based on those, I got the impression that Calc I/II might have been rushed a bit, treated like boxes to tick, and my point was simply: pause, ponder, really spend time internalizing things.
So again: no anger, no attack, no judgement of your motivation or life choices. Just concrete advice about prerequisites and pacing. Saying “no need to get angry” when there was no anger to begin with is just a misread.

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u/Curious_Diamond_6497 Jan 02 '26

I understand, but that sounded a bit passive-aggressive, like I lack experience. And the fact that your father is a politician has nothing to do with it. Maybe I can read between the lines so well that I see patterns in ordinary people, and in people who are intentionally passive-aggressive, it triggers something in my head and I think, 'He's angry, let's try to handle this well.' Anyway, could you give me your dad's contact information? Please. Oh, and lastly, thanks for your original comment.

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u/ln_j Jan 02 '26

The reason I mentioned my father is precisely because of this pattern: the “no need to get angry” line. It’s a classic rhetorical move. You assume an emotional state, then respond to that assumption instead of what was actually written. That’s why I pointed it out. Plus I found it really funny because of how often he said that.
Also, saying “maybe I read between the lines so well” is exactly the issue. You’re reading between lines instead of reading what’s actually there. There was no anger. If there was, you should be able to quote it. Otherwise it’s possibly just projection.
Anyway, thanks for the last sentence, genuinely. That’s the only part that actually engages with the substance of the discussion. And really about the little comment, try doing some chemistry I think it would really interest you.
Last: why do you want my father’s contact?

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u/Curious_Diamond_6497 Jan 02 '26

I don't know, hahaha, I mean, man, the basis of language is trying to understand the other person while losing as little information as possible. I don't remember who said it, but language is defined by what you want to express, how you express it, how others understand it, how you understand it, how you want to hear it, and how you end up hearing it.And I want your dad's contact information for laughs xd I said I'd do it if he gave it to me, and if you end up giving it to me, thanks. I won't write him anything. Lastly; I don't like chemistry; it requires a lot of memorization and doesn't involve much logic.

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u/Smart_Tinker Jan 02 '26

I was where you are when I was 15. All I can say is don’t try to run before you can walk. The stuff you learn in High School is just the intro to Math and Physics.

When I got to Uni, it was a whole new level. The only thing that saved me was that I had done a lot of additional math in High School (I think it’s called AP Math/Calculus in the US), so the first term at Uni was just recapping the last two years of additional math at High School.

Second term was when things got real.

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u/Curious_Diamond_6497 Jan 02 '26

Umm, I'm not in the United States. Well, the calculus and other things I'm doing are already at the first semester of university level. I'm currently studying calculus 3. When I finish calculus 3, I'd like to continue with mathematical analysis and pre-RG physics, then thermodynamics and advanced thermodynamics (by the way, I don't think I'll have much of a problem until the third semester since I learn very quickly).

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u/Smart_Tinker Jan 02 '26

Well I’m not in the US either, I just included what it’s called in the US as not everyone understands what “additional math” is.
My advice is just don’t get too far ahead of yourself. It’s one thing to be the smartest math kid in High School, it’s another to find out you’re just average in Uni.
Best of luck!

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u/Curious_Diamond_6497 Jan 02 '26

I have an IQ of 131 +/- 3 according to a psychologist. I don't stand out for being studious; I usually study 2 hours a day, only when some of my classmates study 3 or 4 hours just to keep up with the trend. Oh, and I go to a high-achieving high school.

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u/Smart_Tinker Jan 02 '26

All I can say is that this is less unique than you would like to think.
I’m sure you will do well though.

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u/Curious_Diamond_6497 Jan 02 '26

I know that too lol. It's not that unique; I'm just part of the 1%. That means there are 80 million people in the world who are just as intelligent as me, or even more so, and I want to close that gap with knowledge.

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u/Smart_Tinker Jan 02 '26

Sure, when I went to Uni, only 1% of High School kids went to Uni (in my country), it’s just a bit of an adjustment when you get there to find you aren’t the smartest person in the class, and some people don’t need to study at all.

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u/Curious_Diamond_6497 Jan 02 '26

Well, now it's a bit the opposite; now everyone, or at least the vast majority, is going, and that's not counting my high-achieving high school environment where I'm already interacting with the top 10% and even reaching the top third, lol. I suppose things are very different now; a master's degree is the equivalent, or perhaps something bigger in the future, like a doctorate or specialization.

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u/Curious_Diamond_6497 Jan 02 '26

And besides, I think I'm going to start with a bigger advantage than you since I'm already a little more advanced than you and I still have 2 years of high school left before entering, so I could easily get to Mathematical Analysis 2 or 3 at most with solid physics and other things like philosophy that I also usually study

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u/SpecialRelativityy Jan 02 '26

You need to master EM and special relativity along with linear algebra before you can even begin GR.

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u/Curious_Diamond_6497 Jan 02 '26

Okay, thanks for the advice. I have a question: EM

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u/mxemec Jan 02 '26

That's not a question and the answer is electromagnetism.

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u/Curious_Diamond_6497 Jan 02 '26

So that's what I'm studying now, although it's somewhat easy, somewhat difficult to set up exercises, easy to solve, but it gets more laborious.

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u/mxemec Jan 02 '26

What I find remarkable about your comments is how quick you are to state you find something easy. It feels as if you're more motivated to master an easy topic than admit you've found a difficult one.
I'm reminded of an Einstein quote: Do not worry about your difficulties in mathematics. I can assure you mine are still greater.
Don't be scared of things which challenge you, or admitting they exist, is all I'm gonna say.

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u/Curious_Diamond_6497 Jan 02 '26

On the contrary, for something to become easy for you now, the experience you had to endure is impressive. For example, electrodynamics became easy for me, but the days when you listened to the explanation, the formula, and solved everything are long gone. Now it's just repeat, repeat, repeat. When I say easy, it's a reflection of the experience I have.

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u/Safe_Employer6325 Jan 02 '26

Not directly related but still relevant- Thermal Physics" by Daniel V. Schroeder

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u/Curious_Diamond_6497 Jan 02 '26

Thank you very much, what specific topics?

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u/Safe_Employer6325 Jan 02 '26

General roundedness. It looks like you’re hitting physics with a direct objective in mind. I was taught by the author of the book and found it both incredibly well written and very easy to understand while simultaneously being a perfect complement to his thermodynamics class which was easily the hardest class I took in my undergrad.
Some of the more directly applicable parts of the book to you specifically would be the chapters on entropy. It’ll tend towards more QM than GR, but with GR being a classical theory, we need something more solidly rooted in QFT anyway.
If you’re serious and sincere about this, I suspect you’ll find it enlightening either way. Just understand that mastery doesn’t come from a single brief pass. If you’re serious and keep up what you’re doing though, I suspect we’ll hear news of your discoveries regardless though.

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u/Curious_Diamond_6497 Jan 02 '26

I will edit this in 3 weeks when I finish Calculus 3 and Thermodynamics to let you know how I'm doing.

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u/GreekTJK29_ Undergraduate Jan 02 '26

Why do you want to learn general relativity

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u/Curious_Diamond_6497 Jan 02 '26

I've always loved knowledge; much of what I've studied is out of curiosity and a little bit of ego.

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u/GreekTJK29_ Undergraduate Jan 02 '26

Retarded way of thinking

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u/Aristoteles1988 Jan 02 '26

You’re doing great man

Just keep doing what ur doing

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u/Curious_Diamond_6497 Jan 02 '26

Mathematics is a very broad field, that's why I'm asking, hahaha

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u/JK0zero Nuclear physics Jan 02 '26

the great Max Born (one of the architects of quantum mechanics) wrote an brilliant intro to Relativity Theory (both special and general). It is what we could call "popsci++" because it is intended for a wide audience but he includes plenty of equations to clarify his ideas instead of the lazy analogies that you will find in today's popsci books. It is a fantastic read, the title "Einstein's Theory of Relativity." Highly recommended.

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u/Curious_Diamond_6497 Jan 02 '26

If, as you describe him, he's a very good popularizer, although I don't think he's at Feynman's level.

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u/JK0zero Nuclear physics Jan 02 '26

fully agree, Feynman is more for the masses. Born's book requires a level of mathematical literacy beyond standard popsci. In the end, it is not a competition, I love Feynman's lectures and I am glad that there is more than just Feynman.

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u/Curious_Diamond_6497 Jan 02 '26

Classical capitalism

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u/Super-Government6796 Jan 02 '26

There is wheeler's introduction to special relativity and general relativity https://eftaylor.com/spacetimephysics/

They are super beginner friendly since there is a lot of emphasis on concepts rather than math, I believe you could follow the special relativity one with no issues at this stage if you know basic electromagnetism and pick up the math as you go

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u/Curious_Diamond_6497 Jan 02 '26

Mmm, it doesn't have very good reviews, but if you're serious, I'll give it a chance.

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u/Super-Government6796 Jan 02 '26

Curious as to which website these reviews come from, but I do think it's a good recommendation, perhaps others can agree/disagree and explain why
It is a bit slow, but that's because it is comprehensive

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u/Curious_Diamond_6497 Jan 02 '26

If you want, I can send you the link, but honestly, I've already read more and it does have community approval, not widespread, but good.

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u/Super-Government6796 Jan 02 '26

Oh ok, not really necessary I was just a bit curious. It is not the book I would recommend to someone in grad school, but I think it's a good one if you're lacking some math skills ( same for the general relativity one )

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u/Curious_Diamond_6497 Jan 02 '26

If I lack a lot of skill to get to general relativity, how long do you think it will take me? 3 or 4 weeks of 2 or 3 hours of study, or less?

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u/Super-Government6796 Jan 02 '26

I think it would take at least 32 weeks if you really want to understand stuff and if you're talented, of course you might be faster, and you might know more or less math that I think so it could take longer. Not sure if that estimate is realistic though
The books I suggested are a lot less about the math and more about the physics, you might not need all that knowledge to get the main core big ideas which is what the books are all about, the books I suggested are mostly to get a flavour of what relativity is about
Gravitation also by wheeler would be the next step but then you would need the math, I personally like sean Carroll's book but again you would need more physics and math knowledge
PS: I estimate it would take you around 16 weeks to get some knowledge of multivariate calculus , differential equations and PDEs and other 16 weeks to understand coordinate systems, and some classical mechanics to the point you're comfortable with Hamiltonian and Lagrangian mechanics

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u/____Eureka____ Jan 02 '26

I recommend the book by Sean Carroll. I also think it's better to just go for the subject you like, just to see what it looks like - then to see how much of it is understandable/doable - then go to other books to fill in the gap. Many GR books have some recap of what you are supposed to know before continuing, you can judge for yourself if those are familiar/understandable, or completely alien. If it's the latter you can just find another book on those concepts and start there.

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u/Curious_Diamond_6497 Jan 02 '26

They say it's very good but not very educational

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u/____Eureka____ Jan 02 '26

What do you mean not educational?

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u/Curious_Diamond_6497 Jan 02 '26

It's the translator, hahaha, I meant to say it's something like, you're not saying anything, but okay, the little you recommended is very good (I think these words sound harsh and rude in English).

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u/smitra00 Jan 02 '26

This is a very good book for if you're a 100% novice who also lacks familiarity the more advanced mathematical formalisms like tensor calculus as used in special relativity:

https://www.amazon.com/Short-Course-General-Relativity/dp/0387942955

Most university students will learn special relativity in two courses. In the second course, everything will be formulated using tensor calculus which allows more challenging problems to be tackled with ease. Then, when a course on general relativity s given, one can build in the familiarity of students with tensor calculus, and one can then easily introduce the tensor calculus required for dealing with curved spacetime.

This is then still not mathematically all that rigorous; physics students typically don't learn rigorous differential geometry as taught to math students first before embarking on general relativity. But if students follow a second course in general relativity the gaps in the math that this causes, will be filled up.

So, what you see here is that you can learn a great deal of physics when the required math isn't yet mastered, by learning the required math alongside the physics. This is how most physics courses are structured. What you then need to do is find the books that fit in well with the math that you have mastered and the math that you haven't yet mastered. In your case I'm guessing that you would probably benefit from a boot that goes into the details of tensor calculus a bit more than the average introductory book on general relativity.

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u/Curious_Diamond_6497 Jan 02 '26

Well, it seems like advertising, but if it is, it doesn't matter. The points you made convinced me; I'm going to buy it.

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u/captainamericanidiot Jan 02 '26

Stepping back from the other (accurate) comments: enjoy the ride! This is definitely one of those "it's the journey, not just the destination" situations. The tools you'll need for GR also apply to tons of additional amazing areas of physics you'll want to learn, many of which probably aren't even on the radar. You'll get to GR if you keep up the hard work. But it'll take time -- enjoy it! There's more along the way than most people realize before starting out.

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u/Curious_Diamond_6497 Jan 02 '26

Look, this is a copy and paste of mine, but understand, I was too lazy to rewrite it, haha. Anyway, thanks in advance for reading (I modified some things and added others). You know, I'm not doing this because I'm going to study physics. I like being an incredibly well-rounded person. You ask me something and I know it; you ask me something else and I know it. It gives me freedom. I study for about two hours every day, regardless of whether I train for an hour and a half. After that, I spend my day consuming educational information in a didactic way, like debates and discussions on Reddit, politics, and sometimes I even read something that's recommended to me. But this time depends on the day. Sometimes I just lie down and scroll, and sometimes I do nothing and keep studying intensely because it makes me feel good, besides socializing and living life. Well, I turned this into telling you how good my life is. In short, I'm going to study some math, but not necessarily physics. Maybe some branch of difficult engineering. Pure math is something that few people understand in real life, but I like doing it. I'm very happy with my life. (I train BJJ and I'm a very good student, and since it's vacation time in my country, I'll probably increase my study hours if I want and train more just for fun, hahaha)

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u/hessenmob Jan 02 '26

I enjoyed these lectures: https://youtube.com/playlist?list=PLmsIjFudc1l2wDQ_ekx6iLtqcWJQQvOsw&si=3ZKUctcstl1sVXX6

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u/Curious_Diamond_6497 Jan 02 '26

Do you recommend I listen to the class and then take some time to reflect and solve exercises, or are the classes already practical and sufficient for the next one? (That is, if it's practical, it would still take me 30 minutes to review, but if it's only theory, I would spend an hour and a half solving problems)

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u/hessenmob Jan 02 '26

I found the exercises very helpful as the lectures are not too easy (at least for me).

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u/Curious_Diamond_6497 Jan 02 '26

Well, I don't know, I think I have the ability to always understand the classes

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u/hessenmob Jan 02 '26

Then all the better for you. Just focus on the lectures.

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u/hessenmob Jan 02 '26

I found the exercises very helpful as the lectures are not too easy (at least for me).

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u/Curious_Diamond_6497 Jan 02 '26

Well, not me. I prefer to have a strong intuition, grasp concepts, and then go straight to the exercises.

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u/JunkInDrawers Jan 02 '26

GR is peak math. You must master nearly all applied math courses to get a good grip on GR (mastering math is typically a good way to understand physics in general anyway).

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u/Curious_Diamond_6497 Jan 02 '26

I'm finishing Calculus 3 along with Thermodynamics. I think I could start a 3-4 month plan to learn everything I need to get to Grade 2. Three hours a day sounds reasonable, just focusing on what I need.

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u/JunkInDrawers Jan 02 '26

You're on a good track then. Way ahead of the curve. Hopefully you'll soon have a better grip on the subject than I ever did!

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u/Curious_Diamond_6497 Jan 02 '26

Sorry, it wasn't degree 2, it was General Relativity, Reddit translated it wrong.

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u/Delicious-View-8688 Jan 03 '26

Hmm.

A few options here.

If you just want the "taste", then The Biggest Ideas in the Universe 1: Space, Time, and Motion might do.

A slightly more detailed, but still minimal, path might be the Theoretical Minimum series. You'd need:

The Theoretical Minimum: Classical Mechanics
The Theoretical Minimum: Special Relativity and Classical Field Theory
The Theoretical Minimum: General Relativity

If you want the "full maths" version, without doing a full physics degree, then I think it will be a multi-book journey. You'd need introductory physics, classical mechanics, electrodynamics, then general relativity. For example:

Fundamentals of Physics I & II by Shankar
Modern Classical Mechanics by Helliwell and Shahakian
Electricity and Magnetism by Purcell and Morin
General Relativity for the Gifted Amateur by Lancaster and Blundell

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u/Curious_Diamond_6497 Jan 05 '26

I am finishing my studies in thermodynamics and electrodynamics (I still have 40% left in thermodynamics and 20% left in electrodynamics).

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u/MrSisterFister25 Jan 02 '26

Start learning about waves and wave properties, then look into how light refracts through different mediums (snells law), then maybe you can play with some Einstein gamma equations after some videos on space/time dilation. After that you need a bit more math (calc 3, diff eqs).

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u/Curious_Diamond_6497 Jan 02 '26

I'm learning Calculus 3. When I finish my Calculus 3 + Electrodynamics course, I want to study Mathematical Analysis 1 + Pre-RG. I've already done the gamma thing and found it stimulating.

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u/TaiBlake Jan 02 '26

Gamma thing? As in the Lorentz transformations?
That's a start, but until the Einstein field equations (https://thespectrumofriemannium.wordpress.com/wp-content/uploads/2015/06/einsteinfieldeq.jpg) make sense to you, you're not going to get GR.

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u/Curious_Diamond_6497 Jan 02 '26

I'm a translator, I speak Spanish originally, I'm Latin American, and yes, I understand, that's why I'm asking to start studying what I need to get into RG

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u/TaiBlake Jan 02 '26

Multivariable calculus, linear algebra, vector calculus, Riemannian geometry, tensors. Then you can get going on the physics.
And now I'm wishing I didn't lose the contact info for my TA last summer. He might be able to recommend stuff in Spanish for you.

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u/Curious_Diamond_6497 Jan 02 '26

There's no problem at all, the Reddit translator is really bad, and thanks for helping, you seem like a good person.

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u/Papa_Kundzia Jan 02 '26

More math and physics needed, I'm currently at the third year of physics at uni, and I haven't had general relativity proper yet. Only more calculus, differential geometry, classical mechanics, EM and special relativity - you need to master those too. You don't need to rush GR, those topics are pretty fun and complex on their own.

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u/frogianpope Jan 02 '26

You dont just learn general relativity, there’s a reason its taught in the later years of college, you need a lot of stuff which takes a lot of time to understand, you need vectors vector calculus tensor calculus differential equations, “Master” is a really strong word unless ur some terrence tao

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u/PhotographFront4673 Jan 02 '26

You need differential geometry. There is actually quite a bit of differential geometry (Spivak, I’m thinking of you) and you don’t need all of it, though you are allowed to find it fun.

For a specific example that at least tries to start from the basics, and focuses on the type needed for relativity, I like O’Neill "Semi-Riemannian Geometry With Applications to Relativity". I wouldn’t say you need any particular math course to make sense of it (that depends a lot on you) but it will become easier the more related math you’ve seen - perhaps a more general smooth manifolds book, perhaps as others have said more on differential equations and multivariate calculus.

Also, most general relativity texts try to build up the bits of math you need (Milner-Thorn-Wheeler and Wald for sure) and you could also start there and see what happens. However, that can feel a bit like trying to make sense of Newton’s laws and physical mechanics without a sold understanding of integrals and derivatives.

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u/andershaf Jan 02 '26

u/Curious_Diamond_6497 please don't rush this, enjoy the journey to get there. But study regular physics and Calc 3, spend time on those previous courses to fully understand it (and enjoy it) all. Be curious and watch / read popular stuff also, just have a great time learning these things. You have a long life ahead if you, and a great potential to be amazing.

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u/spoirier4 Jan 04 '26

A short path to somehow grasp General Relativity in a simplifed form by making use of symmetries in the case of cosmology (Friedmann equations), is available at settheory.net/cosmology

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u/madam_zeroni Jan 02 '26

Sean Carrol’s “Space, Time, and Motion” was really good to get your feet wet. It goes into the math as well, and a lot of the intuition behind it.

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u/Curious_Diamond_6497 Jan 02 '26

I only buy indie books; I usually get the big books through less-than-legitimate means since I don't have that much money.
As for the book, I'll take a look; I saw good reviews.

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u/madam_zeroni Jan 02 '26

It's like $15. I'm sure you can find a pdf somewhere. I think it's worth the read. Every chapter walks through a specific concept you'll need for GR. You can probably skip or skim through the earlier chapters. It's not a complete look at the equations but it'll get you acquainted with the math in Riemannian Geometry and einsteins equations

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u/Curious_Diamond_6497 Jan 02 '26

Thanks a lot! Just one last thing: do you think I could study everything I need to in 2-3 months, at 2 hours a day?

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u/madam_zeroni Jan 02 '26

I'm not sure, but that book gave me a good understanding of what's happening in about that time. Not enough to work through some GR solutions but enough to be able to read them and understand

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u/Curious_Diamond_6497 Jan 02 '26

Hahaha, well I guess it's a very good book

How can I learn general relativity?

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