Spherically symmetric dynamical horizons

TL;DR

This paper characterizes the conditions under which spherically symmetric initial data evolve into dynamical horizons, providing a systematic way to construct and identify such horizons in spherically symmetric spacetimes.

Contribution

It derives a single master equation governing spherically symmetric dynamical horizons and establishes necessary and sufficient conditions for their existence and construction.

Findings

Reduction of constraints to a second order linear master equation

Systematic construction method for spherically symmetric dynamical horizons

Necessary and sufficient conditions for horizons in spherically symmetric spacetimes

Abstract

We determine sufficient and necessary conditions for a spherically symmetric initial data set to satisfy the dynamical horizon conditions in the spacetime development. The constraint equations reduce to a single second order linear master equation, which leads to a systematic construction of all spherically symmetric dynamical horizons (SSDH) satisfying certain boundedness conditions. We also find necessary and sufficient conditions for a given spherically symmetric spacetime to contain a SSDH.