Lower-dimensional Limits of Cubic Lovelock Gravity

TL;DR

This paper derives lower-dimensional limits of cubic Lovelock gravity via regularized Kaluza-Klein reduction and studies the resulting static black hole solutions, revealing consistency with naive limits except in 4D for non-planar horizons.

Contribution

It introduces a regularized reduction method for cubic Lovelock gravity and analyzes black hole solutions in these lower-dimensional theories.

Findings

Solutions match naive limits for planar black holes in 4D.

In 4D, non-planar black holes do not match naive limits.

Provides a consistent framework for lower-dimensional Lovelock gravity.

Abstract

In this paper, we obtain the lower-dimensional limits $(p=2,3,4,5,6)$ of cubic Lovelock gravity through a regularized Kaluza-Klein reduction. By taking a flat internal space for simplicity, we also study the static black hole solutions in the resulting theories. We show that the solutions match with the ones obtained from the "naive limit" of $D$-dimensional equation for the metric function, which is obtained by first scaling the relevant couplings by a factor of $\frac{1}{D-p}$ and then taking the limit $D\to p$, with one important exception: In 4D, one obtains the expected solution only for the black hole with a planar horizon.