Abstract
In this paper, we construct a new class of charged rotating dilaton black brane solutions, with complete set of rotation parameters, which is coupled to a nonlinear Maxwell field. The Lagrangian of the matter field has the form of the power-law Maxwell field. We study the causal structure of the spacetime and its physical properties in ample details. We also compute thermodynamic and conserved quantities of the spacetime such as the temperature, entropy, mass, charge, and angular momentum. We find a Smarr-formula for the mass and verify the validity of the first law of thermodynamics on the black brane horizon. Finally, we investigate the thermal stability of solutions in both canonical and grand-canonical ensembles and disclose the effects of dilaton field and nonlinearity of Maxwell field on the thermal stability of the solutions. We find that for $\alpha \leq 1$, charged rotating black brane solutions are thermally stable independent of the values of the other parameters. For $\alpha>1$, the solutions can encounter an unstable phase depending on the metric parameters.
Highlights
On the other side, there is strong evidence on the observational side that our Universe is currently experiencing a phase of accelerating expansion [7,8,9,10,11,12,13]
There is strong evidence on the observational side that our Universe is currently experiencing a phase of accelerating expansion [7,8,9,10,11,12,13]. This acceleration phase cannot be explained through the standard model of cosmology, which is based on the Einstein theory of general relativity
Some physicists have become convinced that the Einstein theory of gravitation cannot give a complete description of what really occurs in our Universe and one needs an alternative theory
Summary
There is strong evidence on the observational side that our Universe is currently experiencing a phase of accelerating expansion [7,8,9,10,11,12,13]. The thermodynamics of higher-dimensional Ricci flat rotating black branes with a conformally invariant power-law Maxwell source in the absence of a dilaton field was studied in [60]. We explored exact topological black hole solutions in the presence of a nonlinear power-law Maxwell source as well as a dilaton field [61] Since these solutions [61] are static, it is worthwhile to construct the rotating version of the solutions. We intend to construct a new class of (n + 1)-dimensional rotating dilaton black branes in the presence of power-law Maxwell field, where we relax the conformally invariant issue for generality. We present the basic field equations of Einstein dilaton gravity with a power-law Maxwell field and find a new class of charged rotating black brane solutions of this theory and investigate their properties. We finish our paper with closing remarks in the last section
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