# Black hole mass can’t be

A singularity doesn’t have mass. Mass is a property of an object that exists in time. A (spacelike, e.g. Schwarzschild) singularity is not an object that exists in time. A singularity is a moment in time when time ends along with mass. Furthermore, a black hole does not have a center. The geometry of the Schwarzschild spacetime inside the horizon is an infinitely long 3-cylinder with a quickly shrinking circumference. Also, no black hole solution is valid inside the horizon, because all solutions assume a static metric, but it is not static inside the horizon.

— safesphere

— May 20, 2019 at 10:38

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And if you wanted to say that the whole mass $M$ is obtained from the singularity, you won’t be able to get a good calculation because the integral over the singularity would be singular. Moreover, the space and time are really interchanged inside the black hole (the signs of the components $grr$ and $gtt$ get inverted for $r < 2GM$) so the exercise is in no way equivalent to a simple 3D volume integral of $M \delta(x) \delta(y) \delta(z)$. The Schwarzschild singularity, to pick the "simplest" black hole, is a moment in time, not a place in space. It is the final moment of life for the infalling observers. In a locally (conformally) Minkowski patch near the singularity with some causally Minkowskian coordinates $t,x,y,z$ and $r = |(x,y,z)|$, the Schwarzschild singularity looks like a $t=t_f$ hypersurface, not as $r=0$.

— Black hole mass can't be visualized as a property of the black hole interior

— Lubos Motl

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2022.11.08 Tuesday ACHK