A Positivity Theorem for Gravitational Tension in Brane Spacetimes

TL;DR

This paper proves a positivity theorem for gravitational tension in certain brane spacetimes, showing that the gravitational contribution to tension is always positive, using spinor techniques.

Contribution

It introduces a positivity theorem for gravitational tension in brane spacetimes, extending the understanding of gravitational charges in these configurations.

Findings

Gravitational tension is positive definite in the studied spacetimes.

The proof employs spinor techniques to establish positivity.

The work relates tension to asymptotic symmetries in brane geometries.

Abstract

We study transverse asymptotically flat spacetimes without horizons that arise from brane matter sources. We assume that asymptotically there is a spatial translation Killing vector that is tangent to the brane. Such spacetimes are characterized by a tension, analogous to the ADM mass, which is a gravitational charge associated with the asymptotic spatial translation Killing vector. Using spinor techniques, we prove that the purely gravitational contribution to the spacetime tension is positive definite.