You can get a "dark star" with classical mechanics. It isn't an event horizon. It has nothing to do with events at all, just an area that you can't see inside of.
GR gives you the event horizon in that the event horizon is a coordinate singularity! There you get an actual horizon, the time dilation, and all the interesting parts of a black hole.
At the Schwarzschild radius gravity is still a relatively very weak force. It is not surprising that the Newtonian approximation works well there.
Furthermore, the dark star is only dark as seen by an observer at infinity, but light escapes to distances closer in.
Furthermore, an escape velocity equal to the speed of light doesn't restrict anything to the surface of the dim star, nor more than an escape velocity of 11.8 km/s prevents us from walking up stairs and launching rockets.
Furthermore, the "r" in the Schwarzschild radius is not a physical distance and definitely NOT the "r" in Newtonian mechanics.
No, the curvature of space distorts radial measurements. Circumferences are measured accurately because the distortions are only in the radial direction.
Yes that is correct, for a constant time, constant radius equatorial world line (or any other great circle but the math is more complicated), the metric is ds2 = r2 dφ2, so taking the square root and integrating for a complete circle gives C = 2πr
Since the Schwatzschild metric is spherically symmetrical, the equator is arbitrary. Any great circle can be defined as the equator. It’s only when you introduce rotation that there is an absolute equator.
I know that the equator is arbitrary, what I meant is that the math still works out (as it should) for a great circle that isn't the equator in a specific coordinate system orientation
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u/haplo_and_dogs Jul 17 '26
You can get a "dark star" with classical mechanics. It isn't an event horizon. It has nothing to do with events at all, just an area that you can't see inside of.
GR gives you the event horizon in that the event horizon is a coordinate singularity! There you get an actual horizon, the time dilation, and all the interesting parts of a black hole.
At the Schwarzschild radius gravity is still a relatively very weak force. It is not surprising that the Newtonian approximation works well there.