Vacuum thin shell solutions in five-dimensional Lovelock gravity

TL;DR

This paper explores vacuum thin shell solutions in five-dimensional Lovelock gravity, revealing new global structures including vacuum wormholes and analyzing their stability and dynamic properties.

Contribution

It introduces novel vacuum shell solutions and demonstrates the existence of spherically symmetric wormholes in five-dimensional Lovelock gravity, expanding the understanding of possible spacetime configurations.

Findings

Vacuum spherically symmetric wormholes exist in this theory.

Both static and dynamical solutions are proven to exist.

New instability modes are identified for certain coupling values.

Abstract

Junction conditions for vacuum solutions in five-dimensional Einstein-Gauss-Bonnet gravity are studied. We focus on those cases where two spherically symmetric regions of space-time are joined in such a way that the induced stress tensor on the junction surface vanishes. So a spherical vacuum shell, containing no matter, arises as a boundary between two regions of the space-time. Such solutions are a generalized kind of spherically symmetric empty space solutions, described by metric functions of the class $C^0$. New global structures arise with surprising features. In particular, we show that vacuum spherically symmetric wormholes do exist in this theory. These can be regarded as gravitational solitons, which connect two asymptotically (Anti) de-Sitter spaces with different masses and/or different effective cosmological constants. We prove the existence of both static and dynamical solutions and discuss their (in)stability under perturbations that preserve the symmetry. This leads us to discuss a new type of instability that arises in five-dimensional Lovelock theory of gravity for certain values of the coupling of the Gauss-Bonnet term.