Resolving the Schwarzschild singularity in both classic and quantum gravity

TL;DR

This paper proposes a dynamic model of collapsing stars that replaces singularities with a quantum breathing ball, offering insights into black hole entropy and information paradox resolution.

Contribution

It introduces a quantum framework for black hole interiors, showing non-singular, oscillating states and quantized micro-states related to horizon size.

Findings

Final state is a periodically oscillating breathing ball.

Number of micro-states grows exponentially with horizon radius.

Provides a quantum explanation for horizon entropy and information preservation.

Abstract

The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work the general dynamic inner metric of collapsing stars with horizons and with non-trivial radial mass distributions. We find that static central singularities are not the final state of the system. Instead, the final state of the system is a periodically zero-cross breathing ball. Through 3+1 decomposed general relativity and its quantum formulation, we establish a functional Schr\"odinger equation controlling the micro-state of this breathing ball and show that, the system configuration with all the matter concentrating on the central point is not the unique eigen-energy-density solution. Using a Bohr-Sommerfield like "orbital" quantisation assumption, we show that for each black hole of horizon radius $r_h$, there are about $e^{r_h^2/\ell^2_\mathrm{pl}}$ allowable eigen-energy-density profile. This naturally leads to physic interpretations for the micro-origin of horizon entropy, as well as solutions to the information missing puzzle involved in Hawking radiations.