Black holes in five-dimensional Palatini $f(R)$ gravity and implications for the AdS/CFT correspondence

TL;DR

This paper explores five-dimensional Palatini $f(R)$ gravity, revealing new second-order theories beyond Lovelock, and discusses their potential implications for the AdS/CFT correspondence without relying on quasi-topological models.

Contribution

It demonstrates that second-order field equations in higher-dimensional modified gravity can arise without assuming metric-affine relations, expanding the scope of theories applicable to AdS/CFT.

Findings

Second-order field equations are not limited to Lovelock Lagrangians.

Palatini $f(R)$ gravity in five dimensions provides alternative models.

Potential new applications in AdS/CFT correspondence exploration.

Abstract

We show that theories having second-order field equations in the context of higher-dimensional modified gravity are not restricted to the family of Lovelock Lagrangians, but can also be obtained if no a priori assumption on the relation between the metric and affine structures of space-time is made (Palatini approach). We illustrate this fact by considering the case of Palatini $f(R)$ gravities in five dimensions. Our results provide an alternative avenue to explore new domains of the AdS/CFT correspondence without resorting to {\it ad hoc} quasi-topological constructions.