Positive energy-momentum theorems for asymptotically AdS spin initial data sets with charge

TL;DR

This paper proves positive energy-momentum theorems for asymptotically AdS spin initial data with charge, establishing non-negativity and a mass-charge inequality under certain energy conditions.

Contribution

It introduces a charged energy-momentum functional for asymptotically AdS initial data and proves its positivity, extending classical results to charged, asymptotically hyperbolic manifolds.

Findings

Energy-momentum functional is non-negative under dominant energy condition.

Establishes a mass-charge inequality for time-symmetric, charged asymptotically hyperbolic manifolds.

Provides a framework for analyzing charged initial data in asymptotically AdS spacetimes.

Abstract

For complete spin initial data sets with an asymptotically anti--de Sitter end, we introduce a charged energy--momentum defined as a linear functional arising from the Einstein--Maxwell constraints. Under a dominant energy condition adapted to the presence of a negative cosmological constant, we establish positive energy--momentum theorems, showing in particular that this functional is non--negative on a natural real cone. We place particular emphasis on the case where the manifold carries a compact inner boundary. In the time--symmetric setting, this yields a mass--charge inequality for asymptotically hyperbolic manifolds with charge.