Static wormhole solution for higher-dimensional gravity in vacuum

TL;DR

This paper presents a new static vacuum wormhole solution in higher odd-dimensional gravity theories, connecting two asymptotically AdS spacetimes with unique geometric and causal properties, including zero mass and smooth Euclidean continuation.

Contribution

It introduces a novel static wormhole solution in higher-dimensional Lovelock gravity, specifically in odd dimensions, with unique geometric and causal features.

Findings

The wormhole connects two asymptotically locally AdS spacetimes.

The Euclidean continuation is smooth with vanishing Euclidean action.

The mass of the wormhole is zero.

Abstract

A static wormhole solution for gravity in vacuum is found for odd dimensions greater than four. In five dimensions the gravitational theory considered is described by the Einstein-Gauss-Bonnet action where the coupling of the quadratic term is fixed in terms of the cosmological constant. In higher dimensions d=2n+1, the theory corresponds to a particular case of the Lovelock action containing higher powers of the curvature, so that in general, it can be written as a Chern-Simons form for the AdS group. The wormhole connects two asymptotically locally AdS spacetimes each with a geometry at the boundary locally given by R times S^{1} times H_{d-3}. Gravity pulls towards a fixed hypersurface located at some arbitrary proper distance parallel to the neck. The causal structure shows that both asymptotic regions are connected by light signals in a finite time. The Euclidean continuation of the wormhole is smooth independently of the Euclidean time period, and it can be seen as instanton with vanishing Euclidean action. The mass can also be obtained from a surface integral and it is shown to vanish.