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As I understand it, we measure things like distance (and volume) by the speed of light. A meter is the distance light travels in 1/299792458 seconds. In "normal space" this is (barely) straightforward, but around black holes it's confusing.

I suppose we reason about black holes by doing external measurements. We have theory that tells us where the event horizon is relative to a center of mass, right? But "inside" that event horizon, the means by which we measure distance and volume itself is nonsense. Is knowing the volume of a black hole using external measurements actually sufficient to know the amount of space inside the event horizon of a black hole?

Or I guess, if a meter is the distance light travels in some time and light takes an undefined or infinite amount of time to travel a meter inside a black hole, then is a black hole "bigger on the inside" (even infinite) than it is on the outside?

Edit: Clarify the question to be about the volume inside the event horizon, not about the volume of the singularity itself.

Qmechanic
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kojiro
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1 Answers1

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A black hole is a point mass, or a singularity. It has an 'infinitely' large density and 'infinitely' small volume. The mass can vary which to me means that the volume and/or density must vary somewhat from black hole to black hole, but that is how they are defined. Although the actual volume of the black hole is infinitely small, it's field effects are much wider. There is a brief article related to this here: https://www.skyandtelescope.com/astronomy-resources/how-big-is-a-black-hole/

benchmuser
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  • Right, my question was poorly phrased -- I was more asking what is the "volume inside the event horizon" I have edited the question to be clearer. – kojiro Apr 10 '19 at 14:33
  • It's not true that the singularity of a (Schwarzschild) black hole is a point, or that it has zero volume. See https://physics.stackexchange.com/questions/144447/is-a-black-hole-singularity-a-single-point –  Apr 10 '19 at 14:39