Positivity of energy for asymptotically locally AdS spacetimes

TL;DR

This paper establishes conditions under which the energy in asymptotically locally AdS spacetimes is well-defined, linking boundary geometry to energy positivity and exploring differences in even and odd dimensions.

Contribution

It derives necessary geometric conditions for the spinorial energy to be well-defined in asymptotically locally AdS spacetimes, including boundary conformal properties.

Findings

Conditions on boundary spinors for energy well-definition

Equivalence of gravitational and spinorial energy in even dimensions

Bounded difference related to conformal anomaly in odd dimensions

Abstract

We derive necessary conditions for the spinorial Witten-Nester energy to be well-defined for asymptotically locally AdS spacetimes. We find that the conformal boundary should admit a spinor satisfying certain differential conditions and in odd dimensions the boundary metric should be conformally Einstein. We show that these conditions are satisfied by asymptotically AdS spacetimes. The gravitational energy (obtained using the holographic stress energy tensor) and the spinorial energy are equal in even dimensions and differ by a bounded quantity related to the conformal anomaly in odd dimensions.