Linear Stability Analysis and the Speed of Gravitational Waves in Dynamical Chern-Simons Modified Gravity

TL;DR

This paper analyzes the stability and propagation speed of gravitational waves in dynamical Chern-Simons gravity, finding stability, light-speed travel in flat spacetime, and mode splitting near black holes with implications for horizon detection.

Contribution

It provides the first linear stability analysis of dynamical Chern-Simons gravity and characterizes gravitational wave speeds and mode splitting in black hole backgrounds.

Findings

Stable linear behavior in considered backgrounds

Gravitational waves travel at light speed in Minkowski spacetime

Mode splitting into subluminal and superluminal speeds near black holes

Abstract

We perform a linear stability analysis of dynamical Chern-Simons modified gravity in the geometric optics approximation and find that it is linearly stable on the backgrounds considered. Our analysis also reveals that gravitational waves in the modified theory travel at the speed of light in Minkowski spacetime. However, on a Schwarzschild background the characteristic speed of propagation along a given direction splits into two modes, one subluminal and one superluminal. The width of the splitting depends on the azimuthal components of the propagation vector, is linearly proportional to the mass of the black hole, and decreases with the third inverse power of the distance from the black hole. Radial propagation is unaffected, implying that as probed by gravitational waves the location of the event horizon of the spacetime is unaltered. The analysis further reveals that when a high frequency, pure gravitational wave is scattered from a black hole, a scalar wave of comparable amplitude is excited, and vice-versa.