Hawking Radiation and Energy Conservation in an Evaporating Black Hole

TL;DR

This paper defines a new Bondi energy in 2D dilatonic gravity, demonstrating its relation to ADM energy and radiation, and explicitly calculates energy recovery in an evaporating black hole model.

Contribution

It introduces a generalized Bondi energy in 2D dilatonic gravity and applies it to an evaporating black hole, linking energy definitions with Hawking radiation.

Findings

Bondi energy equals ADM energy minus radiation energy at null infinity

Infalling matter energy is fully recovered through Hawking radiation and thunderpop

Explicit calculation in the RST model confirms energy conservation during evaporation

Abstract

We define the Bondi energy for two-dimensional dilatonic gravity theories by generalizing the known expression of the ADM energy. We show that our definition of the Bondi energy is exactly the ADM energy minus the radiation energy at null infinity. An explicit calculation is done for the evaporating black hole in the RST model with the Strominger's ghost decoupling term. It is shown that the infalling matter energy is completely recovered through the Hawking radiation and the thunderpop.