Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity

TL;DR

This paper investigates how Schwarzschild black holes behave in dynamical Chern-Simons gravity, revealing unique gravitational wave signatures that could be detected by observatories like LIGO or LISA, and discusses stability and ghost issues.

Contribution

It provides the first detailed analysis of black hole perturbations in dynamical Chern-Simons gravity, highlighting observable imprints on gravitational waveforms and stability conditions.

Findings

Black hole perturbations are stable with ringdown behavior.

Gravitational waveforms are influenced by scalar field coupling.

Ghost instabilities occur for negative coupling constants.

Abstract

Dynamical Chern-Simons gravity is an extension of General Relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard General Relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun for Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods.