Loosely trapped surface for slowly rotating black hole

TL;DR

This paper constructs and analyzes marginal loosely trapped surfaces in slowly rotating Kerr black holes, revealing an infinite family with a unique maximal surface at higher order perturbations.

Contribution

It introduces a perturbative method to construct marginal LTSs in Kerr spacetime and identifies a unique maximal LTS among infinitely many.

Findings

All marginal LTSs have the same area at leading order.

A unique maximal marginal LTS is determined at higher order.

Infinite number of marginal LTSs exist in Kerr spacetime.

Abstract

We construct the marginal loosely trapped surface (marginal LTS) for the Kerr spacetime with a small Kerr parameter perturbatively, where the LTS condition is saturated. An LTS is a surface that specifies the strong gravity region, which is a generalization of the photon sphere in the Schwarzschild spacetime. It turns out that there are an infinite number of marginal LTSs. At the leading order of the small Kerr parameter, all of the marginal LTSs have the same area. However, one can see that the maximal marginal LTS among them is uniquely determined at the higher order.