Approximate analytical description of apparent horizons for initial data with momentum and spin

TL;DR

This paper develops an approximate analytical method to describe the apparent horizons of initial data for rotating and moving black holes, revealing how their shape depends on the orientation of spin and momentum.

Contribution

It introduces an approximate analytical approach to characterize apparent horizons for black holes with arbitrary spin and momentum orientations in conformally flat initial data.

Findings

The shape of the apparent horizon depends on the angle between spin and momentum.

A dimple forms on the horizon's 2-sphere geometry, influenced by the orientation.

The method applies to conformally flat initial metrics for black holes.

Abstract

We construct analytical initial data for a slowly moving and rotating black hole for generic orientations of the linear momentum and the spin. We solve the Hamiltonian constraint approximately and work out the properties of the apparent horizon and show the dependence of its shape on the angle between the spin and the linear momentum. In particular a dimple, whose location depends on the mentioned angle, arises on the 2-sphere geometry of the apparent horizon. We exclusively work in the case of conformally flat initial metrics.