Loosely trapped surface and dynamically transversely trapping surface in Einstein-Maxwell system

TL;DR

This paper investigates the properties of loosely trapped surfaces and dynamically transversely trapping surfaces in Einstein-Maxwell systems, establishing Penrose-like inequalities that include electromagnetic field corrections and analyzing these in specific black hole spacetimes.

Contribution

It proves Penrose-like inequalities for LTSs and DTTSs in Einstein-Maxwell systems, incorporating electromagnetic corrections and providing numerical evaluations in two-black-hole solutions.

Findings

Penrose-like inequalities include electromagnetic corrections.

The inequalities for LTSs are tighter than naive bounds.

Numerical evaluation performed in Majumdar-Papapetrou spacetimes.

Abstract

We study the properties of the loosely trapped surface (LTS) and the dynamically transversely trapping surface (DTTS) in Einstein-Maxwell systems. These concepts of surfaces were proposed by the four of the present authors in order to characterize strong gravity regions. We prove the Penrose-like inequalities for the area of LTSs/DTTSs. Interestingly, although the naively expected upper bound for the area is that of the photon sphere of a Reissner-Nordstroem black hole with the same mass and charge, the obtained inequalities include corrections represented by the energy density or pressure/tension of electromagnetic fields. Due to this correction, the Penrose-like inequality for the area of LTSs is tighter than the naively expected one. We also evaluate the correction term numerically in the Majumdar-Papapetrou two-black-hole spacetimes.