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

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 black hole 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(B)(2)tau diverges. We also compute the di ff usion constants for the case that the DC conductivity is fi nite but in the absence of momentum relaxation.