Communications in Analysis and Geometry

Volume 29 (2021)

Number 1

Stationary axisymmetric black holes with matter

Pages: 19 – 76

DOI: https://dx.doi.org/10.4310/CAG.2021.v29.n1.a2

Authors

Otis Chodosh (Department of Mathematics, Princeton University, Princeton, New Jersey, U.S.A.)

Yakov Shlapentokh-Rothman (Department of Mathematics, Princeton University, Princeton, New Jersey, U.S.A.)

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 is fundamental to our construction [3] 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.

Received 29 October 2015

Accepted 23 May 2018

Published 11 March 2021