Thermodynamics of Gauss-Bonnet-Dilaton Lifshitz Black Branes

Abstract

We explore an effective supergravity action in the presence of a massless gauge field which contains the Gauss-Bonnet term as well as a dilaton field. We construct a new class of black brane solutions of this theory with the Lifshitz asymptotic by fixing the parameters of the model such that the asymptotic Lifshitz behavior can be supported. Then we construct the well-defined finite action through the use of the counterterm method. We also obtain two independent constants along the radial coordinate by combining the equations of motion. Calculations of these two constants at infinity through the use of the large-$r$ behavior of the metric functions show that our solution respects the no-hair theorem. Furthermore, we combine these two constants in order to get a constant $C$ which is proportional to the energy of the black brane. We calculate this constant at the horizon in terms of the temperature and entropy, and at large-$r$ in terms of the geometrical mass. By calculating the value of the energy density through the use of the counterterm method, we obtain the relation between the energy density, the temperature, and the entropy. This relation is the generalization of the well-known Smarr formula for AdS black holes. Finally, we study the thermal stability of our black brane solution and show that it is stable under thermal perturbations.

11 pages, version to be published in Phys. Rev. D

References in corpus (13)

• Slowly-Rotating Black Holes in Einstein-Dilaton-Gauss-Bonnet Gravity: Quadratic Order in Spin Solutions
• Holographic stress tensor for non-relativistic theories
• Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions I -- Asymptotically Flat Black Holes --
• Thermodynamics of Rotating Charged Black Branes in Third Order Lovelock Gravity and the Counterterm Method
• Thermal behavior of charged dilatonic black branes in AdS and UV completions of Lifshitz-like geometries
• Thermodynamics of topological nonlinear charged Lifshitz black holes
• Quasi-Topological Lifshitz Black Holes
• Counterterm Method in Lovelock Theory and Horizonless Solutions in Dimensionally Continued Gravity
• Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions III -- Asymptotically AdS Black Holes with $k=\pm 1$ --
• Nonlinearly charged Lifshitz black holes for any exponent $z>1$
• Thermodynamics of nonlinear charged Lifshitz black branes with hyperscaling violation
• Thermodynamics of charged Lifshitz black holes with quadratic corrections
• Global Structure of Black Holes in String Theory with Gauss-Bonnet Correction in Various Dimensions

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• An analytical approximation for the Einstein-dilaton-Gauss-Bonnet black hole metric
• Black hole solutions in Gauss-Bonnet-massive gravity in the presence of power-Maxwell field
• Charged scalar quasi-normal modes for linearly charged dilaton-Lifshitz solutions
• Critical behaviour of Lifshitz dilaton black holes
• Holographic Conductivity for Logarithmic Charged Dilaton-Lifshitz Solutions
• AdS and Lifshitz Scalar Hairy Black Holes in Gauss-Bonnet Gravity
• Optical properties of Born-Infeld-dilaton-Lifshitz holographic superconductors
• Charged black holes in a generalized scalar-tensor gravity model
• On double-black hole solutions of the Einstein-Maxwell-Dilaton theory in five dimensions
• Generalized Thermodynamic Properties of Lifshitz black holes