Attractive gravity probe surface in Einstein-Maxwell system

TL;DR

This paper establishes new areal inequalities for various types of attractive gravity probe surfaces in Einstein-Maxwell systems, extending concepts like extremality and the Penrose inequality to broader contexts including weak gravity regions and anti-de Sitter spacetimes.

Contribution

It generalizes the Riemannian Penrose inequality to include electric, magnetic, and other contributions, defining extremality for surfaces beyond black hole horizons.

Findings

Derived areal inequalities for five types of attractive gravity probe surfaces.

Extended extremality conditions to surfaces in weak gravity regions.

Generalized inequalities to asymptotically locally anti-de Sitter spacetimes.

Abstract

We derive areal inequalities for five types of attractive gravity probe surfaces, which were proposed by us in order to characterize the strength of gravity in different ways including weak gravity region, taking into account of contributions of electric and magnetic charges, angular momentum, gravitational waves, and matters. These inequalities are generalizations of the Riemannian Penrose inequality for minimal surfaces, and lead to the concept of extremality for a given surface whose condition is given in terms of the gravitational mass and the electromagnetic charges. This means that the extremality is a characteristic property not only of black hole horizons or minimal surfaces but also of surfaces in weak gravity region. We also derive areal inequalities and extremality conditions for surfaces in asymptotically locally anti-de Sitter spacetimes.