The positive energy theorem for asymptotically anti-de Sitter spacetimes

TL;DR

This paper proves a positive energy inequality for asymptotically anti-de Sitter spacetimes, generalizing previous results and establishing a geometric invariant related to energy-momentum.

Contribution

It extends the positive energy theorem to arbitrary t-slices in AdS spacetime and identifies the determinant of the energy-momentum endomorphism as a geometric invariant.

Findings

Established energy-momentum inequality for asymptotically AdS initial data.

Generalized previous inequalities to arbitrary t-slices.

Identified the determinant of energy-momentum endomorphism as a geometric invariant.

Abstract

We establish the inequality for Henneaux-Teitelboim's total energy-momentum for asymptotically anti-de Sitter initial data sets which are asymptotic to arbitrary $t$-slice in anti-de Sitter spacetime. In particular, when $t=0$, it generalizes Chru\'{s}ciel-Maerten-Tod's inequality in the center of AdS mass coordinates. We also show that the determinant of energy-momentum endomorphism ${\bf Q}$ is the geometric invariant of asymptotically anti-de Sitter spacetimes.