Black Hole evaporation in semi-classical approach

TL;DR

This paper investigates black hole evaporation using a semi-classical approach, demonstrating that black holes ultimately vanish by solving complex field equations with a novel method involving dynamical horizons in Vaidya spacetime.

Contribution

The paper introduces a new method to solve fourth-order field equations, proving black holes can evaporate completely within a semi-classical framework.

Findings

Black holes emit thermal radiation at null infinity.

Black holes eventually vanish after evaporation.

A new solution method for complex field equations is proposed.

Abstract

As well as known, the black hole evaporation problem is famous problem. Because the S.W.Hawking found the black holes emit light at the future null infinity as a thermal radiation \cite{H}, we think that the black holes may be vanish. However, to prove this problem, we should solve field equation, i.e. forth order partial differential equations \cite{Ford}\cite{BD}. However, we can find a method to solve this equation, and we could prove that the black holes finally vanish. To solve this problem we use dynamical horizons equation in the Vaidya spacetime.