Dynamical horizons and Super-Translation transitions of the horizon

TL;DR

This paper establishes a condition to identify when supertranslations are induced during the evolution of horizons, providing a way to analyze horizon transitions and their symmetries.

Contribution

It introduces a specific condition that determines supertranslation induction during horizon evolution and illustrates it with spherically symmetric dynamical horizons.

Findings

Supertranslations can be induced during horizon evolution.

A condition for supertranslation induction is preserved along isolated horizons.

Spherical symmetry simplifies the analysis of supertranslation conditions.

Abstract

A condition is defined which determines if a supertranslation is induced in the course of a general evolution from one isolated horizon phase to another via a dynamical horizon. This condition fixes preferred slices on an isolated horizon and is preserved along an Isolated Horizon. If it is not preserved, in the course of a general evolution, then a supertranslation will be said to have been induced. A simple example of spherically symmetric dynamical horizons is studied to illustrate the conditions for inducing supertranslations.