Lifshitz-like black branes in arbitrary dimensions and the third law of thermodynamics

Original Abstract

In this paper we present a systematic construction of an(isotropic) black brane solutions in arbitrary spacetime dimensions $D$ in particular, with Lifshitz-like asymptotics. Two distinct holographic models are considered. The first model involves a scalar field with a potential coupled to two Maxwell fields, allowing for both electric and magnetic charges. The second model includes a scalar field, a Maxwell field, and a three-form field strength of a Kalb-Ramond field. For each model, exact solutions for the metric, scalar field, gauge fields, and coupling functions are derived, incorporating anisotropic scaling exponents and general warp factors, including Gaussian forms. The results generalize previously known five-dimensional anisotropic black brane solutions to arbitrary dimensions. We show that the third law of thermodynamics, which requires entropy to vanish as temperature approaches zero, is satisfied for a certain range of parameters in both models. However, for specific warp factors or coupling constants, the entropy-temperature relation exhibits non-monotonic or multi-valued behavior, suggesting the possibility of phase transitions and a violation of the third law.