Quasinormal modes of Schwarzschild black holes in projective invariant Chern-Simons modified gravity

TL;DR

This paper extends Chern-Simons modified gravity to a metric-affine framework with projective invariance, deriving perturbative solutions for torsion and nonmetricity, and analyzes quasinormal modes of Schwarzschild black holes.

Contribution

It introduces a novel metric-affine formulation of Chern-Simons gravity with projective invariance and studies black hole quasinormal modes within this framework.

Findings

Scalar field exhibits dynamics without kinetic term

Computed quasinormal frequencies numerically

Compared results with metric-only approach

Abstract

We generalize the Chern-Simons modified gravity to the metric-affine case and impose projective invariance by supplementing the Pontryagin density with homothetic curvature terms which do not spoil topologicity. The latter is then broken by promoting the coupling of the Chern-Simons term to a (pseudo)-scalar field. The solutions for torsion and nonmetricity are derived perturbatively, showing that they can be iteratively obtained from the background fields. This allows us to describe the dynamics for the metric and the scalar field perturbations in a self-consistent way, and we apply the formalism to the study of quasinormal modes in a Schwarzschild black hole background. Unlike in the metric formulation of this theory, we show that the scalar field is endowed with dynamics even in the absence of its kinetic term in the action. Finally, using numerical methods we compute the quasinormal frequencies and characterize the late-time power law tails for scalar and metric perturbations, comparing the results with the outcomes of the purely metric approach.