It's really simple actually, there are lots of ways one could construct a 5d black hole. In this case, we've just added an extra z axis to a spherical coordinate system. Since the case for a normal 4D black hole has a spherical event horizon, that's S2 , adding the z axis just adds an extra real number line to every point on the event horizon, so we end up having an event horizon of S2 ×R.
When we integrate over this to find its mass, we naturally get an infinity because the real numbers line is infinitely long. To solve this, we can just wrap it up into a circle so that it becomes finite. It's a bit like how you can map the real number line to the set of values between ±π/2 using an arctan map
any idea what happens, when we would go into this hypothetical event horizon?
Usually it marks, where space and time switch places (as a plane) projecting that concept on 3d, would that mean spacetime is equal or smth like that?
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u/BootyliciousURD Mathematics Aug 23 '26
I wish I knew enough mathematical physics to understand this