Nonlinear electrodynamics and thermodynamic geometry of rotating dilaton black branes

Abstract

We construct a new class of rotating dilaton solutions in the presence of logarithmic nonlinear electrodynamics. These solutions represent black branes with flat horizon and contain k = [(n − 1)/2] rotation parameters in n-dimensional spacetime where [x] is the integer part of x. We study the causal structure of the spacetime and calculate thermodynamic and conserved quantities and show that these quantities satisfy the first law of thermodynamics on the black brane horizon,Then, we study geometrical approach towards thermodynamics by choosing an appropriate geometrical metric. We show that the singularity of the Ricci scalar coincides exactly with the phase transition points. We observe that our system encounters two types of phase transitions depending on the metric parameters. For the first one the heat capacity is zero and for the second one the heat capacity diverges. In the first kind of phase transition, the brane has a transition from an unstable non-physical to a stable physical state. In the second type of phase transition the brane moves from a stable to an unstable state. Finally, we comment on the dynamical stability of the obtained solutions under perturbations in four dimensions.

Thermodynamics and reentrant phase transition for logarithmic nonlinear charged black holes in massive gravity

“…Lifshitz-dilaton black holes/branes coupled to LNE have been investigated in [34]. Magnetic rotating dilaton strings and charged rotating dilaton black strings in Einstein gravity with LNE electrodynamics have been found in [35] and [36], respectively. In the context of Lovelock gravity, authors of [37] explored magnetic brane solutions in the presence of LNE.…”