On energy bounds in asymptotically locally AdS spacetimes

TL;DR

This paper establishes positive energy theorems and BPS inequalities for asymptotically locally AdS spacetimes, including cases with magnetic fields, using geometric and spinor techniques.

Contribution

It provides the first complete proofs of BPS inequalities in 4D and 5D minimal gauged supergravity, extending results to locally AdS spacetimes with specific boundary geometries.

Findings

Positive energy theorems for certain asymptotically locally AdS spacetimes.

First complete proofs of BPS inequalities in 4D and 5D supergravity.

Generalization of BPS bounds to spacetimes with magnetic fields.

Abstract

This work considers positive energy theorems in asymptotically, locally AdS spacetimes. Particular attention is given to spacetimes where conformal infinity has compact, Einstein cross-sections admitting Killing or parallel spinors; a positive energy theorem is derived for such spacetimes in terms of geometric data intrinsic to the cross-section. This is followed by the first complete proofs of the BPS inequalities in (the bosonic sectors of) 4D and 5D minimal, gauged supergravity, including with magnetic fields, provided the Maxwell field is exact. The BPS inequalities are proven for asymptotically AdS spacetimes, but also generalised to the aforementioned class of asymptotically, locally AdS spacetimes.