Scalarization of Chern-Simons Kerr Black Hole Solutions and Wormholes

TL;DR

This paper analyzes scalarization effects on rotating Chern-Simons black holes and wormholes, providing analytic solutions for slow rotation, exploring energy condition violations, and constructing wormhole solutions with axion fields.

Contribution

It extends previous work by deriving all-order analytic expressions for slowly rotating black holes and constructing wormhole solutions influenced by axion fields in Chern-Simons gravity.

Findings

Analytic expressions for slowly rotating black holes near the horizon.

Chern-Simons gravity violates energy conditions, leading to axionic hair.

Wormhole solutions require counter-rotation and show no backreaction in slow rotation.

Abstract

Chern-Simons gravity rotating Kerr-type black hole solutions are revisited from the point of view of their scalarization, namely examining the back reaction of pseudoscalar axion fields on the rotating geometry. To lowest order in an angular momentum expansion, and a long range approximation for both the axion field configuration and its back reaction onto the metric, such solutions had been discussed for the first time in the context of string theory. In this work, we extend the analysis to give analytic expressions for slowly rotating black holes outside the horizon, which formally include an all order expansion in inverse powers of the radial distance from the centre of the black hole, which allows to approach arbitrarily close the horizon. We also discuss in some detail the way Chern-Simons gravity violates the energy conditions, which leads to secondary axionic hair of the rotating black hole solutions. This discussion is extended to studies of wormhole solutions, which we construct in this article via the thin-shell procedure and we demonstrate that the presence of the axion field enforces the two black hole solutions to be counter-rotating and for slow rotation, there is no backreaction of the Cotton tensor on the thin-shell of the wormhole.