A new proof for non-occurrence of trapped surfaces and information paradox

TL;DR

This paper provides a simple mathematical proof that trapped surfaces do not form during spherical gravitational collapse, implying that black holes with finite mass cannot exist and resolving the information paradox.

Contribution

It introduces a novel, assumption-free proof demonstrating the non-formation of trapped surfaces in spherical collapse, challenging traditional black hole models.

Findings

Trapped surfaces do not form in spherical gravitational collapse.

Black holes with finite mass are mathematically impossible under these conditions.

The absence of trapped surfaces eliminates the information paradox.

Abstract

We present here a very simple, short and new proof which shows that no trapped surface is ever formed in spherical gravitational collapse of isolated bodies. Although this derivation is of purely mathematical nature and without any assumption, it is shown, in the Appendix, that, physically, trapped surfaces do not form in order that the 3 speed of the fluid as measured by an observer at a fixed circumference coordinate $R$ (a scalar), is less than the speed of light $c$. The consequence of this result is that, mathematically, even if there would be Schwarzschild Black Holes, they would have unique gravitational mass M=0. Recall that Schwazschild BHs may be considered as a special case of rotating Kerr BHs with rotation parameter a=0. If one would derive the Boyer-Lindquist metric [1] in a straight forward manner by using the Backlund transformation[2], one would obtain a= M sin phi where phi is the azimuth angle. This relation demands that BHs have unique mass M=0 (along with a=0) which in turn confirms that there cannot be any trapped surface in realistic gravitational collapse where the fluid has real pressure and density. Since there is no trapped surface and no horizon there is no Information Paradox in the first place.