# Where is the mass of a Schwarzschild black hole located?

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The entropy of a Schwarzschild black hole is located near the horizon, and the moment of inertia of a Schwarzschild black hole is $MR^2$. Both aspects imply that the mass of a Schwarzschild black hole is distributed across the horizon and near the horizon. But a Nobel prize was just given, in 2020, for a black hole singularity theorem.

Is the black hole mass located near the center, or it is located near the horizon?

recategorized Nov 8, 2020

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A particle dropping into a Schwarzschild black hole takes an infinite time to reach the horizon if observed from the outside. Thus, if a Schwarzschild black hole forming in a collapse is observed, this would suggest that, at any finite time, some mass at least is located outside the horizon, near to it.

On the other hand, if you look at the pure Schwarzschild solution, this is based on an energy-momentum tensor which vanishes everywhere, in particular at the horizon.

The singularity theorems show that solutions to the Einstein field equations may have singularities under generic conditions. The relevance of this is that singularities are not artifacts which appear only under very special symmetry conditions (which conditions might be considered without physical relevance in real astrophysical situations).

answered Nov 7, 2020 by (80 points)

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