Weighing the Black Hole via Quasi-local Energy

Abstract

We set to weigh the black holes at their event horizons in various spacetimes and obtain masses which are substantially higher than their asymptotic values. In each case, the horizon mass of a Schwarzschild, Reissner-Nordstr{\"o}m, or Kerr black hole is found to be twice the irreducible mass observed at infinity. The irreducible mass does not contain electrostatic or rotational energy, leading to the inescapable conclusion that particles with electric charges and spins cannot exist inside a black hole. The is proposed as the External Energy Paradigm. A higher mass at the event horizon and its neighborhood is obligatory for the release of gravitational waves in binary black hole merging. We describe how these mass values are obtained in the quasi-local energy approach and applied to the black holes of the first gravitational waves GW150914.