Thermodynamics of rotating solutions in (n+1)-dimensional Einstein-Maxwell-dilaton gravity

TL;DR

This paper constructs and analyzes charged, rotating black brane solutions in higher-dimensional Einstein-Maxwell-dilaton gravity, exploring their thermodynamic properties, stability, and phase behavior.

Contribution

It introduces new non-asymptotically flat, non-(A)dS black brane solutions and examines their thermodynamics and stability, including a stability phase transition based on the dilaton coupling.

Findings

Solutions can represent black branes, extremal black branes, or naked singularities.

Thermodynamic quantities satisfy the first law of thermodynamics.

System is thermally stable for alpha < 1 and unstable for alpha > 1.

Abstract

We construct a class of charged, rotating solutions of (n+1)-dimensional Einstein-Maxwell-dilaton gravity with Liouville-type potentials and investigate their properties. These solutions are neither asymptotically flat nor (anti)-de Sitter. We find that these solutions can represent black brane, with two inner and outer event horizons, an extreme black brane or a naked singularity provided the parameters of the solutions are chosen suitably. We also compute temperature, entropy, charge, electric potential, mass and angular momentum of the black brane solutions, and find that these quantities satisfy the first law of thermodynamics. We find a Smarr-type formula and perform a stability analysis by computing the heat capacity in the canonical ensemble. We find that the system is thermally stable for alpha <1, while for alpha >1 the system has an unstable phase. This is incommensurate with the fact that there is no Hawking-Page phase transition for black objects with zero curvature horizon.