Conformally flat black hole initial data with one cylindrical end

Abstract

We give a complete analytical proof of the existence and uniqueness of extreme-like black hole initial data for Einstein equations, which possess a cylindrical end, analogous to extreme Kerr, extreme Reissner–Nördstrom and extreme Bowen–York's initial data. This extends and refines a previous result (Dain and Clement 2009 Class. Quantum Grav. 26 035020) to a general case of conformally flat, maximal initial data with angular momentum, linear momentum and matter.