Revisiting Lifshitz-type solutions in $R^2$-corrected gravity

TL;DR

This paper explores new higher-dimensional Lifshitz solutions in $R^2$-corrected gravity, including product manifolds and hyperscaling solutions, and discusses their thermodynamical properties.

Contribution

It introduces novel product manifold and hyperscaling Lifshitz solutions in $R^2$-corrected gravity, expanding the understanding of such geometries.

Findings

New product manifold solutions of the form $Li_{m}\times \Omega_{(n-m)}$.

Hyperscaling Lifshitz solutions for arbitrary $z$.

Analysis of thermodynamical properties of static and stationary solutions.

Abstract

In this work, we investigate higher-dimensional Lifshitz-type topological static and stationary solutions of $R^2$-corrected gravity theory using the language of differential forms. We obtain new product manifold solutions of the form $Li_{m}\times \Omega_{(n-m)}$ , where $Li_m$ represents an $m$-dimensional Lifshitz type submanifold and $\Omega_{(n-m)}$ denotes $(n-m)$-dimensional compact constant curvature manifold. In addition, we present hyperscaling Lifshitz solutions for arbitrary Lifshitz parameter $ z $. We also discuss some thermodynamical properties of both static and stationary solutions, including extremal cases.