Hoop conjecture for colliding black holes : non-time-symmetric initial data

TL;DR

This paper tests the hoop conjecture for colliding black holes with relativistic motion using non-time-symmetric initial data, comparing two mass definitions to determine apparent horizon formation.

Contribution

It systematically investigates the hoop conjecture for dynamic black hole systems with momentum, highlighting the effectiveness of Hawking mass over ADM mass in horizon detection.

Findings

Hawking mass better predicts apparent horizons in dynamic scenarios.

Both mass definitions generally agree on the hoop conjecture.

The hoop conjecture holds for a wider parameter range with Hawking mass.

Abstract

The hoop conjecture is well confirmed in momentarily static spaces, but it has not been investigated systematically for the system with relativistic motion. To confirm the hoop conjecture for non-time-symmetric initial data, we consider the initial data of two colliding black holes with momentum and search an apparent horizon that encloses two black holes. In testing the hoop conjecture, we use two definitions of gravitational mass : one is the ADM mass and the other is the quasi-local mass defined by Hawking. Although both definitions of gravitational mass give fairly consistent picture of the hoop conjecture, the hoop conjecture with the Hawking mass can judge the existence of an apparent horizon for wider range of parameters of the initial data compared to the ADM mass.