Narrow Results

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–Nordström, 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. This 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 horizon mass values are obtained in the quasi-local energy approach and applied to the black holes of the first gravitational waves GW150914.

A new paradigm for black holes is introduced. It is known as the External Energy Paradigm. The paradigm asserts that all energies of a black hole are external quantities; they are absent inside the horizon. These energies include constituent mass, gravitational energy, electrostatic energy, rotational energy, heat energy, etc. As a result, quantum particles with charges and spins cannot exist inside the black hole. To validate the conclusion, we derive the moment of inertia of a Schwarzschild black hole and find that it is exactly equal to mass $\times$ (Schwarzschild radius)², indicating that all mass of the black hole is located at the horizon. This remarkable result can resolve several long-standing paradoxes in black hole theory; such as why entropy is proportional to area and not to volume, the singularity problem, the information loss problem and the perplexing firewall controversy.

A new theorem for black holes is found. It is called the horizon mass theorem. The horizon mass is the mass which cannot escape from the horizon of a black hole. For all black holes, neutral, charged or rotating, the horizon mass is always twice the irreducible mass observed at infinity. Previous theorems on black holes are: (i) the singularity theorem, (ii) the area theorem, (iii) the uniqueness theorem, (iv) the positive energy theorem. The horizon mass theorem is possibly the last general theorem for classical black holes. It is crucial for understanding Hawking radiation and for investigating processes occurring near the horizon.

We evaluate the mass of the black holes of GW150914 at their event horizons via quasi-local energy approach and obtain the values of 71 and 57 solar masses, compared to their asymptotic values of 36 and 29 units, respectively, as reported by LIGO. A higher mass at the event horizon is compulsory in order to overcome the huge negative gravitational potential energy surrounding the black holes and allow for the emission of gravitational waves during merging. We estimate the initial mass of the stars which collapsed to form the black holes from the horizon mass and obtain the impressive values of 95 and 76 solar masses for these progenitor stars.

We investigate the energy distribution of a black hole in various spacetimes as reckoned by a distant observer using the quasi-local energy approach. In each case the horizon mass of a black hole: neutral, charged or rotating, is found to be twice the irreducible mass observed at infinity. This is known as the Horizon Mass Theorem. As a consequence, the electrostatic energy and the rotational energy of a general black hole are all external quantities. Matter carrying charges and spins could only lie outside the horizon. This result could resolve several long-standing paradoxes related to known black hole properties; such as why entropy is proportional to area and not to volume, the information loss problem, the firewall problem, the internal structure and the thin shell model of a black hole.

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–Nordström, 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. This 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 horizon mass values are obtained in the quasi-local energy approach and applied to the black holes of the first gravitational waves GW150914.