Black hole initial data with a horizon of prescribed intrinsic and extrinsic geometry

TL;DR

This paper develops a method to construct 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 both intrinsic and extrinsic horizon geometry in initial data construction.

Findings

Successfully prescribes horizon geometry with the PDE method.

Provides a more direct control over horizon geometry than conformal methods.

Enhances initial data construction for black hole simulations.

Abstract

The purpose of this work is to construct asymptotically flat, time symmetric initial data with an apparent horizon of prescribed intrinsic and extrinsic 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.