Quasilocal inequalities for attractive gravity probe surface

TL;DR

This paper investigates local and quasilocal inequalities related to attractive gravity probe surfaces, introducing improved concepts and establishing bounds on their size and area using various definitions of local mass.

Contribution

It introduces enhanced definitions of LTS and AGPS surfaces and proves new inequalities relating their geometric properties to local mass measures.

Findings

Derived inequalities for LTS and AGPS sizes and areas.

Established relations between geometric properties and local/quasilocal mass.

Proposed improved LTS+ and AGPS+ concepts with proven inequalities.

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.