Self-properties of codimension-2 braneworlds

TL;DR

This paper explores the properties of codimension-2 braneworlds within Lovelock gravity, revealing their embedding in black hole spacetimes, their self-accelerating and self-tuning solutions, and the implications for four-dimensional gravity.

Contribution

It introduces a classification of maximally symmetric braneworld solutions in Lovelock theory, highlighting their embedding in black hole geometries and their self-accelerating and self-tuning properties.

Findings

Braneworld solutions are embedded in Wick-rotated black hole spacetimes.

Some solutions exhibit self-acceleration and self-tuning.

Induced gravity on the brane arises from bulk Lovelock terms.

Abstract

We consider four-dimensional de Sitter, flat and anti de Sitter branes embedded in a six-dimensional bulk spacetime whose dynamics is dictated by Lovelock theory. We find, applying a generalised version of Birkhoff's theorem, that all possible maximally symmetric braneworld solutions are embedded in Wick-rotated black hole spacetimes of Lovelock theory. These are warped solitonic spaces, where the horizons of the black hole geometries correspond to the possible positions of codimension-2 branes. The horizon temperature is related via conical singularities to the tension or vacuum energy of the branes. We classify the braneworld solutions for certain combinations of bulk parameters, according to their induced curvature, their vacuum energy and their effective compactness in the extra dimensions. The bulk Lovelock theory gives an induced gravity term on the brane, which, we argue, generates four-dimensional gravity up to some distance scale. As a result, some simple solutions, such as the Lovelock corrected Schwarzschild black hole in six dimensions, are shown to give rise to self-accelerating braneworlds. We also find that several other solutions have self-tuning properties. Finally, we present regular gravitational instantons of Lovelock gravity and comment on their significance.