Weighing the Black Hole via Quasi-local Energy

TL;DR

This paper calculates black hole masses at their horizons using quasi-local energy, revealing they are twice the irreducible mass and proposing the External Energy Paradigm, with implications for gravitational wave emissions.

Contribution

It introduces a method to measure black hole horizon masses that are higher than their asymptotic values, supporting the External Energy Paradigm and explaining gravitational wave energy release.

Findings

Horizon mass is twice the irreducible mass for various black holes.

Horizon mass exceeds asymptotic mass, implying additional energy near the horizon.

Application to GW150914 black holes supports the proposed mass measurement approach.

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.