On the "Einstein-Gauss-Bonnet Gravity in Four Dimension"

TL;DR

This paper demonstrates that for Einstein-Gauss-Bonnet gravity in four dimensions to have a well-defined linearized gravitational wave equation, the spacetime must be locally conformally flat.

Contribution

It establishes a necessary geometric condition (local conformal flatness) for the viability of linearized gravitational waves in this modified gravity theory.

Findings

Spacetimes in 4D Einstein-Gauss-Bonnet gravity must be locally conformally flat.

Ensures the existence of a well-defined linearized gravitational wave equation.

Provides geometric constraints for this gravity model.

Abstract

To ensure the existence of a well defined linearized gravitational wave equation, we show that the spacetimes in the so-called "Einstein-Gauss-Bonnet gravity in four dimension" have to be locally conformally flat.