Conformally flat black hole initial data, with one cylindrical end

TL;DR

This paper provides a rigorous proof of existence and uniqueness for a class of conformally flat black hole initial data with cylindrical ends, extending previous results to more general cases including angular momentum, linear momentum, and matter.

Contribution

It offers a complete analytical proof for the existence and uniqueness of extreme-like black hole initial data with cylindrical ends, generalizing prior work to include additional physical parameters.

Findings

Proves existence and uniqueness of the initial data

Extends previous results to more general initial data

Includes cases with angular momentum, linear momentum, and matter

Abstract

We give a complete analytical proof of existence and uniqueness of extreme-like black hole initial data for Einstein equations, which possess a cilindrical end, analogous to extreme Kerr, extreme Reissner Nordstrom, and extreme Bowen-York's initial data. This extends and refines a previous result \cite{dain-gabach09} to a general case of conformally flat, maximal initial data with angular momentum, linear momentum and matter.