Generalized Laws of Black Hole Thermodynamics and Quantum Conservation Laws on Hawking Radiation Process

TL;DR

This paper extends classical black hole thermodynamics laws to the interior horizon, generalizes the first law to quantum form, and derives quantum conservation laws for black hole evaporation, reaffirming the Bekenstein-Hawking entropy relation.

Contribution

It introduces a quantum extension of black hole thermodynamics laws and establishes quantum conservation laws during black hole evaporation.

Findings

Classical laws extended to interior horizons.

First law generalized to quantum form.

Quantum conservation laws derived for evaporation.

Abstract

Four classical laws of black hole thermodynamics are extended from exterior (event) horizon to interior (Cauchy) horizon. Especially, the first law of classical thermodynamics for Kerr-Newman black hole (KNBH) is generalized to those in quantum form. Then five quantum conservation laws on the KNBH evaporation effect are derived in virtue of thermodynamical equilibrium conditions. As a by-product, Bekenstein-Hawking's relation $ S=A/4 $ is exactly recovered.