Hyperscaling-violating Lifshitz Solutions in Cubic Gravity

TL;DR

This paper explores Lifshitz and hyperscaling-violating Lifshitz solutions within cubic gravity, extending black hole solutions and identifying specific conditions for their existence in various dimensions.

Contribution

It extends black hole solutions in cubic gravity to arbitrary dynamical exponents and identifies conditions for hyperscaling violation in different dimensions.

Findings

Extended black hole solutions valid for any dynamical exponent z.

Existence of solutions only for specific hyperscaling exponents in 4 and 5 dimensions.

Lifshitz and Schwarzschild-AdS solutions found for certain parameter values.

Abstract

Considering the cubic theory of gravity which has been constructed in \cite{myers}, we study the existence of Lifshitz and hyper scaling violating Lifshitz solutions. We firstly extend the black hole solution of \cite{myers} and find that such extended solutions are valid for any value of dynamical exponent $z$. Next, we examine the existence of the AdS black hole solution with non-zero hyperscaling-violating exponent $\theta$ and general dynamical exponent $z$. We find that the solutions do exist only for $\theta=0,3$ in 4 dimension and $\theta=0,4$ in 5 dimension. In particular, when $\theta=3(4)$ in $4(5)$ dimension, we have Lifshitz and Schwarzschild-AdS black hole solution solution for $z=\{0,1\}$.