A new energy inequality in AdS

TL;DR

This paper derives a new energy inequality in asymptotically Anti-de Sitter spacetimes relating the minimum energy to the area of certain minimal surfaces, extending concepts similar to the Penrose inequality.

Contribution

It introduces a novel energy inequality in AdS spacetimes connecting minimal surface areas to lower bounds on energy, generalizing Penrose-like bounds.

Findings

Derived the minimum energy as a function of minimal surface area.

Established an inequality analogous to the Penrose inequality in AdS.

Provided a framework for analyzing initial data with minimal surfaces in AdS.

Abstract

We study time symmetric initial data for asymptotically AdS spacetimes with conformal boundary containing a spatial circle. Such $d$-dimensional initial data sets can contain $(d-2)$-dimensional minimal surfaces if the circle is contractible. We compute the minimum energy of a large class of such initial data as a function of the area $A$ of this minimal surface. The statement $E \ge E_{min}(A)$ is analogous to the Penrose inequality which bounds the energy from below by a function of the area of a $(d-1)$-dimensional minimal surface.