Stationary axisymmetric black holes with matter
General Relativity and Quantum Cosmology
2015-10-28 v1 Mathematical Physics
Analysis of PDEs
Differential Geometry
math.MP
Abstract
We provide a geometric framework for the construction of non-vacuum black holes whose metrics are stationary and axisymmetric. Under suitable assumptions we show that the Einstein equations reduce to an Einstein-harmonic map type system and analyze the compatibility of the resulting equations. This framework will be fundamental to our forthcoming construction of metric-stationary axisymmetric bifurcations of Kerr solving the Einstein--Klein--Gordon system, and as such, we include specializations of all of our formulas to the case of a time-periodic massive scalar field.
Keywords
Cite
@article{arxiv.1510.08024,
title = {Stationary axisymmetric black holes with matter},
author = {Otis Chodosh and Yakov Shlapentokh-Rothman},
journal= {arXiv preprint arXiv:1510.08024},
year = {2015}
}