Scalarization of Chern-Simons Kerr Black Hole Solutions and Wormholes

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.

Axion induced angular momentum reversal in Kerr-like black holes

“…In the generic CS gravity theory, slowly rotating black hole solutions, in the presence of axion fields back reacting on the geometry, have been recently investigated in [15], extending non-trivially previous results [5][6][7][8][9], [16][17][18]. In [15], the back reaction of the axionic field on the slowly-rotating background metric has been studied to arbitrary order in perturbation theory of an appropriate parameter, γ, proportional to the square of the axion-CS interaction coupling. Such an expansion allows one to go arbitrarily close to the horizon of the hairy (with axion-hair [7][8][9]) black hole.…”

“…In the case of the Kerr black hole, the total angular momentum is given by M a, where M is the mass and a the angular parameter of the rotating black hole. In this respect we stress that in [15], the presence of the axion field coupled to the CS term, which back reacts on the Kerr Black-hole background, implies that the total angular momentum consists of the contributions of both the axion field and the hairy Kerr-like black hole itself, which arises as a consequence of the axionic back reaction on the geometry.…”

“…In this work we extent the study in [15] on the axion-modified-Kerr black hole system by searching for potentially observable effects associated with bound trajectories of satellites in such backgrounds. As in [15], a key rôle in the analysis will be played by the aforementioned perturbative parameter γ, which is proportional to the coupling of the axion field with the CS term and inversely proportional to the square of the total energy of the spacetime.…”

“…In this work we extent the study in [15] on the axion-modified-Kerr black hole system by searching for potentially observable effects associated with bound trajectories of satellites in such backgrounds. As in [15], a key rôle in the analysis will be played by the aforementioned perturbative parameter γ, which is proportional to the coupling of the axion field with the CS term and inversely proportional to the square of the total energy of the spacetime. We stress that it is this dimensionless parameter, rather than the coupling constant itself, that appears in the correction function of the modified Kerr-like black hole solution and measures the strength of the backreaction on the geometry.…”

Lorentz Symmetry Violation in String-Inspired Effective Modified Gravity Theories

“…to be determined "phenomenologically" in various contexts (e.g., rotating black holes and wormholes, beyond string theory, as in [91,92,93]).…”