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

.

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

.

.

2022.11.08 Tuesday ACHK