Black Hole Initial Data with a Horizon of Prescribed Geometry

TL;DR

This paper develops a new method for constructing initial data for black holes with a specified horizon geometry using a parabolic PDE, offering more precise control than traditional conformal approaches.

Contribution

It introduces a novel approach employing a parabolic PDE to prescribe horizon geometry directly, improving upon the conformal method's limitations.

Findings

Successfully constructs initial data with prescribed horizon geometry

Demonstrates the method's ability to specify intrinsic horizon geometry precisely

Provides a new tool for black hole initial data modeling

Abstract

The purpose of this work is to construct asymptotically flat, time symmetric initial data with an apparent horizon of prescribed intrinsic geometry. To do this, we use the parabolic partial differential equation for prescribing scalar curvature. In this equation the horizon geometry is contained within the freely specifiable part of the metric. This contrasts with the conformal method in which the geometry of the horizon can only be specified up to a conformal factor.