Quasi-Local Energy of a Rotating Object Described by Kerr Spacetime

TL;DR

This paper computes the Brown-York quasi-local energy for Kerr black holes without simplifying assumptions, providing an analytic expression that could impact astrophysics and particle modeling.

Contribution

It presents a direct calculation of quasi-local energy for Kerr spacetime with a general approach, including an explicit analytic form.

Findings

Analytic expression involving elliptic integrals for Kerr quasi-local energy

No assumptions on angular momentum or radial coordinate in the calculation

Potential applications in astrophysics and elementary particle modeling

Abstract

The Brown-York quasi-local energy of a rotating black hole described by the Kerr metric and enclosed by a fixed-radius surface is calculated by direct computation. No special assumptions on the angular momentum or the radial coordinate in Boyer-Lindquist coordinates were placed. The arbitrary reference term has been set to zero. The result may be relevant for applications in astrophysics, for modeling elementary particles or for extensions of the framework of quasi-local quantities. An analytic expression in terms of incomplete elliptic integrals is given.