Stationary Lifshitz black holes of R^2-corrected gravity theory

TL;DR

This paper generalizes static Lifshitz black holes in R^2-corrected gravity to include rotation, providing exact solutions that encompass the BTZ black hole as a special case, thus broadening the understanding of such solutions.

Contribution

It introduces a new class of stationary Lifshitz black hole solutions in R^2 gravity, extending previous static solutions and connecting to the BTZ black hole in three dimensions.

Findings

Derived exact stationary Lifshitz black hole solutions.

Showed solutions reduce to BTZ black hole in specific limits.

Expanded the landscape of analytic solutions in R^2 gravity.

Abstract

In this short note, I present a generalization of a set of static D-dimensional (D >= 3) Lifshitz black holes, which are solutions of the gravitational model obtained by amending the cosmological Einstein theory with the addition of only the curvature-scalar-squared term and that are described by two parameters, to a more general class of exact, analytic solutions that involves an additional parameter which now renders them stationary. In the special D=3 and the dynamical exponent z=1 case, the parameters can be adjusted so that the solution becomes identical to the celebrated BTZ black hole metric.