Brown-York Energy in Spacetimes with Horizon

TL;DR

This paper derives a straightforward relationship linking the variation of Brown-York energy near a horizon to the change in the area of the enclosing two-surface, providing insights into gravitational energy in horizon spacetimes.

Contribution

It introduces a simple formula connecting energy change and area variation in spacetimes with horizons, advancing understanding of gravitational energy.

Findings

Established a direct relation between energy change and area variation.

Provided a new perspective on energy in horizon-adjacent regions.

Simplified the calculation of energy changes near horizons.

Abstract

We obtain a simple relationship between the change in the Brown-York energy inside of a closed two-surface just outside of a horizon of spacetime, and the change in the area of that two-surface.