Quasilocal inequalities for attractive gravity probe surface

TL;DR

The paper investigates how to quantify gravity strength in local and quasilocal regions using LTS and AGPS, and extends these notions to LTS+ and AGPS+ defined via null expansions. It derives quasilocal and areal inequalities based on local energy density and quasilocal masses, including a width bound 2G ΔM_eff ≤ ΔL and corresponding area bounds. It then defines LTS+ and AGPS+ and proves analogous inequalities, culminating in a Hawking-mass-based Penrose-like bound for AGPS+ and, for α = 0, A ≤ 4π (3G m_H(S))^2. The results constrain gravitational collapse and the structure of compact objects across strong and weak gravity regimes and provide a unified framework for quasilocal gravity probes.

Abstract

We discuss the local and quasilocal properties of the loosely trapped surface (LTS) and the attractive gravity probe surface (AGPS), which have been proposed to characterize the strength of gravity in both strong and weak gravity regions using the mean curvature. In terms of local mass defined in a region surrounded by the two AGPSs and of Geroch quasilocal mass, we present several inequalities concerning their size and area, which are of particular interest. We also propose the improved concepts of the LTS/AGPS, which we call LTS Plus (LTS+) and AGPS Plus (AGPS$+$), defined in terms of expansions of outgoing and ingoing null geodesic congruences on those surfaces. Then, the similar inequalities are proven in terms of appropriately defined local mass and the Hawking quasilocal mass.