The day of reckoning: The value of the integration constant in the vacuum Schwarzschild solution

TL;DR

This paper argues that the Schwarzschild black hole solution implies a zero mass and entropy, challenging the existence of traditional black holes and suggesting they are actually hot compact objects, thereby resolving the information paradox.

Contribution

It demonstrates that the integration constant in the Schwarzschild solution must be zero, leading to the conclusion that black holes as traditionally conceived do not exist.

Findings

Schwarzschild black holes have zero mass and entropy.

Event horizons merge with singularities, removing the black hole boundary.

Black hole candidates are likely hot compact objects, not true black holes.

Abstract

The stongest theoretical support for Schwarzschild Black Holes (SBHs) is the existence of vacuum Schwarzschild/Hilbert solution. The integration constant alpha_0 in this solution is interpreted as the mass of the BH. But by equating the 4-volumes (an INVARIANT) associated with the Schwarzschild and the Eddington-Finkelstein metrics, we directly obtain here the stunning result that SBHs have the unique mass, M_0 = 0! Thus the Event Horizon of a SBH (R_g = 2M_0 =0) gets merged with the central singularity at R=0 and, after 90 years, the mysterious EH indeed gets erased from the non-singular R >0 region of a completely empty (R_0=0) spherical POINT MASS spacetime in accordance with the intuition of the founders of GR. Consequently the entropy of SBHs have the unique value of zero, which instantly removes the quantum mechanical``information paradox'' and the apparent conflict between GR and QM, the two pillars of modern physics. This direct result firmly establishes the exciting fact, as far as isolated bodies are concerned, GR is a singularity free theory even at the classical level! The Black Hole Candidates with mass M >0 are thus NOT BHs and instead could be HOT compact objects whose possibility has so far been overlooked in favour of COLD Neutron Stars or BHs. With alpha_0 =0, the BH paradigm collapses instantly because it was built with the ASSUMPTION alpha_0 >0. This result is dedicated to the occurrence of 100 years of Relativity.