Time-Periodic Einstein--Klein--Gordon Bifurcations of Kerr

TL;DR

This paper constructs new stationary, axisymmetric black hole solutions with time-periodic scalar fields bifurcating from Kerr, demonstrating instability of Kerr under certain scalar field conditions.

Contribution

It introduces a novel family of solutions to Einstein--Klein--Gordon equations that bifurcate from Kerr, showing non-stability for specific Klein--Gordon masses.

Findings

Existence of bifurcating solutions with non-zero, time-periodic scalar fields.

Kerr black holes are not asymptotically stable under these scalar perturbations.

New solutions are asymptotically flat, stationary, and axisymmetric.

Abstract

We construct one-parameter families of solutions to the Einstein--Klein--Gordon equations bifurcating off the Kerr solution such that the underlying family of spacetimes are each an asymptotically flat, stationary, axisymmetric, black hole spacetime, and such that the corresponding scalar fields are non-zero and time-periodic. An immediate corollary is that for these Klein--Gordon masses, the Kerr family is not asymptotically stable as a solution to the Einstein--Klein--Gordon equations.