The Volume Inside a Black Hole

Details The Volume Inside a Black Hole The Volume Inside a Black Hole

2008-01-11

arxiv.org/abs/0801.1734v1

Gen.Rel.Grav.42:63-76,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, 5 figures

Scientific paper

10.1007/s10714-009-0814-x

The horizon (the surface) of a black hole is a null surface, defined by those hypothetical "outgoing" light rays that just hover under the influence of the strong gravity at the surface. Because the light rays are orthogonal to the spatial 2-dimensional surface at one instant of time, the surface of the black hole is the same for all observers (i.e. the same for all coordinate definitions of "instant of time"). This value is 4*(pi)* (2Gm/c^2)^2 for nonspinning black holes, with G= Newton's constant, c= speed of light, and m= mass of the black hole. The 3-dimensional spatial volume inside a black hole, in contrast, depends explicitly on the definition of time, and can even be time dependent, or zero. We give examples of the volume found inside a standard, nonspinning spherical black hole, for several different standard time-coordinate definitions. Elucidating these results for the volume provides a new pedagogical resource of facts already known in principle to the relativity community, but rarely worked out.

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