# Lovelock Branes

## TL;DR

This paper investigates conditions for brane-like solutions in Lovelock gravity, revealing that base metrics must be proportional to Einstein metrics, with special cases allowing more flexible solutions, thus advancing understanding of higher curvature gravity solutions.

## Contribution

It establishes general conditions for Lovelock brane solutions, identifying subclasses of Einstein and universal metrics, and explores special coupling cases for simplified solution construction.

## Key findings

- Base metrics must be proportional to Einstein metrics for generic Lovelock couplings.
- Universal metrics are included as solutions, previously studied in quantum corrections.
- Special tuning of couplings reduces constraints, enabling straightforward brane solution construction.

## Abstract

We study the problem of finding brane-like solutions to Lovelock gravity, adopting a general approach to establish conditions that a lower dimensional base metric must satisfy in order that a solution to a given Lovelock theory can be constructed in one higher dimension. We find that for Lovelock theories with generic values of the coupling constants, the Lovelock tensors (higher curvature generalizations of the Einstein tensor) of the base metric must all be proportional to the metric. Hence, allowed base metrics form a subclass of Einstein metrics. This subclass includes so-called `universal metrics', which have been previously investigated as solutions to quantum-corrected field equations. For specially tuned values of the Lovelock couplings, we find that the Lovelock tensors of the base metric need to satisfy fewer constraints. For example, for Lovelock theories with a unique vacuum there is only a single such constraint, a case previously identified in the literature, and brane solutions can be straightforwardly constructed.