Propagation Speed of Gravitational Wave in Scalar--Einstein--Gauss-Bonnet Gravity

TL;DR

This paper investigates conditions under which gravitational waves propagate at the speed of light in scalar-Einstein-Gauss-Bonnet gravity, revealing differences between cosmological and black hole backgrounds and implications for realistic black hole models.

Contribution

It constructs a class of sEGB gravity models where gravitational wave speed matches light speed and analyzes the differences in wave speed conditions between cosmological and black hole spacetimes.

Findings

Gravitational wave speed equals light speed in certain sEGB models with inflation.

Discrepancies in wave speed conditions between FRLW universe and black hole backgrounds.

Black hole solutions in sEGB gravity are incompatible with light-speed gravitational waves unless specific scenarios are introduced.

Abstract

The propagation speed of the gravitational wave in scalar--Einstein--Gauss-Bonnet (sEGB) gravity is generally different from that of light. Using differential equation conditions for the speed of gravitational waves to coincide with the light speed in the expanding universe, we constructed a general class of sEGB gravities where this condition is satisfied and realistic inflation occurs. It is demonstrated that the condition that the speed of gravitational wave coincides with that of the light in the Friedmann-Lema\^{i}tre-Robertson-Walker (FRLW) universe is always different from the condition for gravitational wave speed in the sEGB black hole background. Moreover, it is shown that when gravitational wave speed in sEGB black hole is equal to the speed of light the black hole spacetime geometry is changing too so that formally there is no solution for such sEGB black hole. This may indicate that sEGB black holes hardly can be considered as realistic black holes unless some reasonable scenario to make gravitational wave speed to be equal to that of light is proposed, at least asymptotically.