Einstein-Bumblebee-Dilaton black hole in Lifshitz spacetimes

TL;DR

This paper explores the thermodynamic phase transitions of Lifshitz black holes in Einstein-dilaton gravity with Lorentz symmetry breaking, revealing Van der Waals-like behavior and critical phenomena.

Contribution

It introduces new asymptotically Lifshitz charged solutions considering Lorentz violation effects and analyzes their thermodynamic phase structure and critical exponents.

Findings

Identified critical points with phase transitions similar to Van der Waals fluids.

Derived the equation of state P(T,V) for Lifshitz black holes with Lorentz violation.

Found critical exponents matching classical Van der Waals system.

Abstract

We investigate the critical behavior of Lifshitz black holes in Einstein-dilaton gravity in the context of spontaneous Lorentz symmetry breaking. Considering the effects of both the bumblebee vacuum expectation value (VEV) and the fluctuations over the VEV, we obtained new asymptotically Lifshitz charged solutions in (3 + 1) dimensions. We consider the longitudinal massive mode of Lorentz Violation (LV) as thermodynamic pressure, leading us to establish an P-V extended phase space. Within this framework, we derive the equation of state P(T,V), and subsequently identify the critical points, which manifest as discontinuities in the specific heat at constant pressure. Following this, we compute the Gibbs free energy, revealing a first-order phase transition within the model. Finally, we determine the critical exponents, demonstrating their equivalence to those observed in the Van der Waals system.