How do Black Holes Spin in Chern-Simons Modified Gravity?

TL;DR

This paper investigates the existence and characteristics of spinning black holes in Chern-Simons modified gravity, revealing that standard solutions are limited and that non-standard configurations may allow for physically relevant black holes.

Contribution

It provides new exact solutions in Chern-Simons gravity and discusses conditions under which spinning black holes can exist in this modified theory.

Findings

Standard scalar choices eliminate all but Schwarzschild solutions.

Exact solutions including black holes and pp-waves are found for non-canonical scalars.

Stationary, axisymmetric spinning black holes likely do not exist without symmetry breaking.

Abstract

No Kerr-like exact solution has yet been found in Chern-Simons modified gravity. Intrigued by this absence, we study stationary and axisymmetric metrics that could represent the exterior field of spinning black holes. For the standard choice of the background scalar, the modified field equations decouple into the Einstein equations and additional constraints. These constraints eliminate essentially all solutions except for Schwarzschild. For non-canonical choices of the background scalar, we find several exact solutions of the modified field equations, including mathematical black holes and pp-waves. We show that the ultrarelativistically boosted Kerr metric can satisfy the modified field equations, and we argue that physical spinning black holes may exist in Chern-Simons modified gravity only if the metric breaks stationarity, axisymmetry or energy-momentum conservation.