Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation

TL;DR

This paper introduces a new class of charged BTZ-like black hole solutions in Lifshitz spacetime with hyperscaling violation and explores their diffusion properties and relation to butterfly velocity, extending previous universal relations.

Contribution

It presents five new charged BTZ-like black hole solutions with a charge-dependent logarithmic term and analyzes their diffusion constants and butterfly velocity relations across various dimensions and parameters.

Findings

Charged BTZ-like solutions characterized by a charge-dependent logarithmic term.

Diffusion constants computed for these solutions, including special cases where $d=\theta$ and $z=2$.

The relation between diffusivity and butterfly velocity exhibits unique behavior in special parameter regimes.

Abstract

We show that there exists a class of charged BTZ-like black hole solutions in Lifshitz spacetime with a hyperscaling violating factor. The charged BTZ is characterized by a charge-dependent logarithmic term in the metric function. As concrete examples, we give five such charged BTZ-like black hole solutions and the standard charged BTZ metric can be regarded as a special instance of them. In order to check the recent proposed universal relations between diffusivity and the butterfly velocity, we first compute the diffusion constants of the standard charged BTZ black holes and then extend our calculation to arbitrary dimension $d$, exponents $z$ and $\theta$. Remarkably, the case $d=\theta$ and $z=2$ is a very special in that the charge diffusion $D_c$ is a constant and the energy diffusion $D_e$ might be ill-defined, but $v^2_B\tau$ diverges. We also compute the diffusion constants for the case that the DC conductivity is finite but in the absence of momentum relaxation.