On the \u201cEinstein\u2013Gauss\u2013Bonnet gravity in four dimension\u201d

Li-Ming Cao,Liang-Bi Wu

doi:10.1140/epjc/s10052-022-10079-5

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.

Highlights

A novel Einstein–Gauss–Bonnet gravity in four dimension has been proposed [1]
The Gauss–Bonnet term is given by LGB = R2 − 4Rμν Rμν + Rμνρσ Rμνρσ
In our manuscript, we further study the restriction on the theory, and point out another unreliability of 4D EGB gravity by studying the behavior of the principal symbol of the linearized perturbation equation under the limit D → 4

Summary

Introduction

A novel Einstein–Gauss–Bonnet gravity in four dimension has been proposed [1]. The so-called four dimensional Einstein–Gauss–Bonnet theory (4D EDB) is defined by considering the limit D → 4. [8], by using the ADM decomposition, the authors proposed that the limit D → 4 depends on the way how to regularize the Hamiltonian or/and the equations of motion These papers all pointed out the non-viability of 4D EDB gravity. Based on these works, in our manuscript, we further study the restriction on the theory, and point out another unreliability of 4D EGB gravity by studying the behavior of the principal symbol of the linearized perturbation equation under the limit D → 4. With a similar logic, we obtained a more restrictive condition, i.e., Eq (2.7), on the metrics of the theory

Examples

Conclusion and discussion