Transversely trapping surfaces: Dynamical version

TL;DR

This paper introduces the concepts of dynamically transversely trapping surfaces (DTTS) and marginally DTTS as new indicators of strong gravity regions, providing theoretical and numerical insights into their properties and potential observational relevance.

Contribution

The paper defines DTTS and marginally DTTS, develops methods to find them in various initial data, and proves a Penrose-like inequality for their area, advancing understanding of strong gravity regions.

Findings

Numerical construction of marginally DTTSs for two-black-hole systems.

Proof of a Penrose-like inequality for DTTS area.

Discussion of the relation between DTTSs and other trapping surfaces.

Abstract

We propose new concepts, a dynamically transversely trapping surface (DTTS) and a marginally DTTS, as indicators for a strong gravity region. A DTTS is defined as a two-dimensional closed surface on a spacelike hypersurface such that photons emitted from arbitrary points on it in transverse directions are acceleratedly contracted in time, and a marginally DTTS is reduced to the photon sphere in spherically symmetric cases. (Marginally) DTTSs have a close analogy with (marginally) trapped surfaces in many aspects. After preparing the method of solving for a marginally DTTS in the time-symmetric initial data and the momentarily stationary axisymmetric initial data, some examples of marginally DTTSs are numerically constructed for systems of two black holes in the Brill-Lindquist initial data and in the Majumdar-Papapetrou spacetimes. Furthermore, the area of a DTTS is proved to satisfy the Penrose-like inequality, $A_0\le 4\pi (3GM)^2$, under some assumptions. Differences and connections between a DTTS and the other two concepts proposed by us previously, a loosely trapped surface [arXiv:1701.00564] and a static/stationary transversely trapping surface [arXiv:1704.04637], are also discussed. A (marginally) DTTS provides us with a theoretical tool to significantly advance our understanding of strong gravity fields. Also, since DTTSs are located outside the event horizon, they could possibly be related with future observations of strong gravity regions in dynamical evolutions.