Loosely trapped surface and dynamically transversely trapping surface in Einstein–Maxwell systems

Abstract

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 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–Nordström 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.