Inside Black Holes, Singularity or Complementarity?

TL;DR

This paper explores two complementary descriptions of black hole microstates using exact solutions to Einstein's equations, linking horizon properties with quantum degeneracy and entropy, and sets the stage for observational tests.

Contribution

It introduces two exact solution families that describe black hole microstates and connects classical solutions with quantum entropy through wave-functional degeneracy.

Findings

Solutions form two complementary descriptions of black hole states.

Bekenstein-Hawking entropy naturally arises from wave-functional degeneracy.

Framework supports future observational tests via gravitational waves and radio bursts.

Abstract

Through two exact solution families to the Einstein equation and the one-to-one correspondence between their free parameters, we show that the ensemble of collapsars with only close-to-implementing horizon in the Schwarzschild time definition and the over-cross-oscillatory solid-balls in the Lemaitre time definition constitute two complementary description for the microscopic state of black holes formed through gravitational collapse. We quantise the solutions in the Schwarzschild time definition and show that the area law formula of Bekenstein-Hawking entropy follows naturally from the wave-functional's degeneracy of the collapsing materials. In two companion works, supports from the gravitational wave of binary merger observation and predictions for the fast radio burst of single body perturbations of this complementarity will be reported independently.