Dynamical horizon of evaporating black hole in Vaidya spacetime

TL;DR

This paper investigates the evolution of an evaporating black hole's mass in Vaidya spacetime using dynamical horizon concepts, deriving an equation that models mass decrease due to Hawking radiation, concluding with a Minkowski final state.

Contribution

It introduces a new equation for black hole mass evolution in Vaidya spacetime considering Hawking radiation using dynamical horizon formalism.

Findings

Black hole mass decreases over time due to Hawking radiation.

Final state of the black hole is Minkowski spacetime.

Derived a specific mass change equation in Vaidya spacetime.

Abstract

We consider how the mass of the black hole decreases by the Hawking radiation in the Vaidya spacetime, using the concept of dynamical horizon equation, proposed by Ashtekar and Krishnan. Using the formula for the change of the dynamical horizon, we derive an equation for the mass incorporating the Hawking radiation. It is shown that final state is the Minkowski spacetime in our particular model.