A lower bound of the Trautman-Bondi energy

TL;DR

This paper derives an energy inequality in the Bondi-Sachs formalism, extends it to the horizon of black holes, and relates it to the Penrose inequality, with tests on the Kerr solution.

Contribution

It introduces a new energy inequality on null surfaces and extends it to event horizons, connecting to the Penrose inequality in general relativity.

Findings

Energy inequality on null surfaces in Bondi-Sachs formalism

Extension of inequality to event horizons of black holes

Validation using Kerr solution in Fletcher-Lun coordinates

Abstract

We obtain an energy inequality on null surfaces $u=const$ in the Bondi-Sachs formalism. We show that for a sufficiently regular event horizon $H$ there is an affine radial coordinate which is constant on $H$. Then the energy inequality can be prolongated to the horizon giving an estimation which is closely related to the Penrose inequality. We test it for the Kerr solution written in the Fletcher-Lun coordinates.