Strictly static spacetimes and positive mass in the Einstein-Gauss-Bonnet theory

TL;DR

This paper proves that in Einstein-Gauss-Bonnet gravity, strictly static, vacuum, asymptotically flat spacetimes with small curvature corrections are necessarily Minkowski spacetime, extending known results from Einstein gravity.

Contribution

It establishes a rigidity result for static vacuum spacetimes in Einstein-Gauss-Bonnet theory, analogous to the classical result in Einstein gravity.

Findings

Strictly static, vacuum, asymptotically flat spacetimes are Minkowski when curvature corrections are small.

The result extends the uniqueness of Minkowski spacetime to Einstein-Gauss-Bonnet theory.

The paper clarifies conditions under which static solutions are trivial in modified gravity theories.

Abstract

In the Einstein gravity, it is well-known that strictly stationary and vacuum regular spacetime should be the Minkowski spacetime. In the Einstein-Gauss-Bonnet theory, we shall show the similar statement, that is, strictly static(no event horizon), vacuum and asymptotically flat spacetimes with conformally static slices are the Minkowski spacetime when the curvature corrections are small.