Formation of dynamically transversely trapping surfaces and the stretched hoop conjecture

TL;DR

This paper introduces the concept of dynamically transversely trapping surfaces (DTTS), explores their formation in various black hole configurations, and proposes a stretched hoop conjecture relating circumference and mass for DTTS formation.

Contribution

It extends the concept of photon spheres to DTTS, studies their formation conditions, and suggests a hoop-like criterion for horizon formation in strong gravity regions.

Findings

DTTS formation condition approximated by $ ext{Circumference} \, \lesssim 6\pi GM$

Configurations with torus topology DTTS inside spherical DTTS identified

Existence of trapped surfaces with torus topology inside spherical trapped surfaces

Abstract

A dynamically transversely trapping surface (DTTS) is a new concept of an extension of a photon sphere that appropriately represents a strong gravity region and has close analogy with a trapped surface. We study formation of a marginally DTTS in time-symmetric, conformally flat initial data with two black holes, with a spindle-shaped source, and with a ring-shaped source, and clarify that $\mathcal{C}\lesssim 6\pi GM$ describes the condition for the DTTS formation well, where $\mathcal{C}$ is the circumference and $M$ is the mass of the system. This indicates that an understanding analogous to the hoop conjecture for the horizon formation is possible. Exploring the ring system further, we find configurations where a marginally DTTS with the torus topology forms inside a marginally DTTS with the spherical topology, without being hidden by an apparent horizon. There also exist configurations where a marginally trapped surface with the torus topology forms inside a marginally trapped surface with the spherical topology, showing a further similarity between DTTSs and trapped surfaces.