The volume inside a black hole

Research Article
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Abstract

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 two-dimensional surface at one instant of time, the surface area 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 4π(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 three-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.

Keywords

Numerical relativity Time slicing Black hole 
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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Center for RelativityUniversity of Texas at AustinAustinUSA

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