Slowly rotating charged BTZ black hole solutions in Palatini Chern-Simons gravity

TL;DR

This paper explores a metric-affine formulation of Chern-Simons gravity in 2+1 dimensions, analyzing perturbations around a charged BTZ black hole to find conditions for stable, rotating solutions with magnetic fields.

Contribution

It introduces a projectively invariant, metric-affine approach to Chern-Simons gravity and develops a perturbative method to study corrections around BTZ black holes.

Findings

Conditions on parameters yield rotating solutions with magnetic fields.

Perturbations remain controlled under specific parameter constraints.

Solutions exhibit smooth decay of fields away from the horizon.

Abstract

We consider a metric-affine formulation of Chern-Simons modified gravity in 2 + 1 dimensions. The theory is built requiring projective invariance, and the structure of the equations is analyzed using a decomposition in terms of scalar, vectorial, and purely tensorial objects. This approach allows us to implement a perturbative approach to study the corrections that emerge around a given background solution, for which we consider a BTZ charged, non-rotating metric. We show that conditions on model parameters are necessary to keep perturbations under control, yielding a rotating solution with a constant angular momentum and magnetic field at the horizon, and a smooth decay further away. We comment on the possibility of going beyond the leading order in perturbations and on its dynamical implications.