On local conservation of information content in Schwarzschild black holes

TL;DR

This paper introduces a geometric phase in general relativity associated with Schwarzschild black hole information, satisfying a local conservation law and linking classical gravity with quantum properties.

Contribution

It proposes a new local conservation law for black hole information content, incorporating a complex-valued function akin to a quantum wave function within Einstein's framework.

Findings

The geometric phase satisfies a local conservation law.

The field equations include a complex function similar to a quantum wave function.

Horizon quantization occurs in units of Planck area.

Abstract

The central equations in classical general relativity are the Einstein Field Equations, which accurately describe not only the generation of pseudo-Riemannian curvature by matter and radiation manifesting as gravitational effects, but more importantly mass-energy dynamics, evolution and distribution on the space-time manifold. Herein, we introduce a geometric phase in general relativity corresponding to Schwarzschild black hole information content. This quantity appropriately satisfies a local conservation law subject to minimal coupling, with other desirable properties such as the quantization of the black hole horizon in units of Planck area. The local conservation law is imposed by field equations, which not only contain the trace of Einstein Field Equations, but also a complex-valued function with properties analogous to the quantum-mechanical wave function. Such success attests to the utility of the proposed field equations in capturing key aspects of quantum gravity theories.