We construct a class of charged, rotating solutions of (n+1)-dimensional Einstein-Maxwelldilaton 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 α ≤ 1, while for α > 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.

We construct a class of charged rotating solutions in (n + 1)-dimensional Maxwell-Brans-Dicke theory with flat horizon in the presence of a quadratic potential and investigate their properties. These solutions are neither asymptotically flat nor (anti)de Sitter. We find that these solutions can present black brane, with inner and outer event horizons, an extreme black brane or a naked singularity provided the parameters of the solutions are chosen suitably. We compute the finite Euclidean action through the use of counterterm method, and obtain the conserved and thermodynamic quantities by using the relation between the action and free energy in grand-canonical ensemble. We find that these quantities satisfy the first law of thermodynamics, and the entropy does not follow the area law.

In this work, the charged black hole solution to the Brans-Dicke gravity theory in the presence of the nonlinear electrodynamics has been investigated. To simplify the field equations, a conformal transformation has been introduced which transforms the Brans-Dicke-Born-Infeld Lagrangian to that of Einstein-dilaton-Born-Infeld theory. A new class of ðn þ 1Þ-dimensional black hole solution has been constructed out as the exact solution to the Brans-Dicke theory in the presence of the Born-Infeld nonlinear electrodynamics. The physical properties of the solutions have been studied. The black hole charge and temperature have been calculated making use of the Gauss's law and the concept of surface gravity, respectively. Also, the black hole mass and entropy have been obtained from geometrical methods. Trough a Smarr-type mass formula as a function of the black hole charge and entropy the black hole temperature and electric potential, as the intensive parameters conjugate to the black hole entropy and charge, have been calculated. The consistency of results of the geometrical and thermodynamical approaches confirms the validity of the first law of black hole thermodynamics for this new black hole solution. Finally, making use of the ensemble canonical method, the local stability or phase transition of the new ðn þ 1Þ-dimensional Brans-Dicke-Born-Infeld black hole solution has been analyzed.

We derive new exact charged rotating solutions of ðn þ 1Þ-dimensional Brans-Dicke theory in the presence of Born-Infeld field and investigated their properties. Because of the coupling between scalar field and curvature, the field equations cannot to be solved directly. Using a new conformal transformation, which transforms the Einstein-dilaton-Born-Infeld gravity Lagrangian to the BransDicke-Born-Infeld gravity one, the field equations are solved. We also compute temperature, charge, mass, electric potential, and entropy; entropy, however, does not obey the area law. These quantities are invariant under conformal transformation and satisfy the first law of thermodynamics.

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