Abstract
In arbitrary dimension, we consider a theory described by the most general quadratic curvature corrections of Einstein gravity together with a self-interacting nonminimally coupled scalar field. This theory is shown to admit five different families of Lifshitz black holes dressed with a nontrivial scalar field. The entropy of these configurations is microscopically computed by means of a higher-dimensional anisotropic Cardy-like formula where the role of the ground state is played by the soliton obtained through a double analytic continuation. This involves to calculate the correct expressions for the masses of the higher-dimensional Lifshitz black hole as well as their corresponding soliton. The robustness of this Cardy-like formula is checked by showing that the microscopic entropy is in perfect agreement with the gravitational Wald entropy. Consequently, the calculated global charges are compatible with the first law of thermodynamics. We also verify that all the configurations satisfy an anisotropic higher-dimensional version of the Smarr formula.
Highlights
Gauge/gravity duality can be extended to nonrelativistic systems by using anisotropic spacetimes
The solitons are obtained from the black holes by means of a double Wick rotation that involves inverting the dynamical critical exponent, as result they enjoy the same sort of uniqueness as the black holes [17]. The robustness of this formula has been successfully tested in a system exhibiting a wide spectrum of Lifshitz configurations as is the case of self-interacting scalar fields nonminimally coupled to New Massive Gravity [18]
We will present the first two classes of solutions that fit within ansatz (4)–(5) and compute their definitive thermodynamic quantities through the preliminary formulas derived in the previous section
Summary
Gauge/gravity duality can be extended to nonrelativistic systems by using anisotropic spacetimes. It becomes important to find specific gravity models that can accommodate the Lifshitz spacetimes together with their black hole extensions recovering the anisotropic scaling asymptotically These so-called Lifshitz black holes are supposed to holographically capture the finite-temperature behavior of their strongly correlated nonrelativistic dual systems. The solitons are obtained from the black holes by means of a double Wick rotation that involves inverting the dynamical critical exponent, as result they enjoy the same sort of uniqueness as the black holes [17] The robustness of this formula has been successfully tested in a system exhibiting a wide spectrum of Lifshitz configurations as is the case of self-interacting scalar fields nonminimally coupled to New Massive Gravity [18]. After some reflections on interesting aspects raised by the new configurations that we include in the conclusions section, we provide several Appendixes for reporting some of the quite involved expressions for the (coupling) constants of the specific solutions
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