Quasitopological Lifshitz dilaton black brane

Abstract

We construct a new class of \((n+1)\)-dimensional Lifshitz dilaton black brane solutions in the presence of the cubic quasitopological gravity for a flat boundary. The related action supports asymptotically Lifshitz solutions by applying some conditions which are used throughout the paper. We have to add a new boundary term and some new counterterms to the bulk action to have finite solutions. Then we define a finite stress tensor complex by which we can calculate the energy density of the quasitopological Lifshitz dilaton black brane. It is not possible to obtain analytical solutions, and so we use some expansions to probe -the behaviors of the functions, both near the horizon and, at the infinity. Combining the equations, we can attain a total constant along the coordinate r. At the horizon, this constant is proportional to the product of the temperature and the entropy and at the infinity, the total constant shows the energydensity of the quasitopological Lifshitz dilaton black brane. Therefore, we can reach a relation between the conserved quantities temperature, entropy and the energy density and get a smarr-type formula. Using the first law of thermodynamics, we can find a relation between the entropy and the temperature and then obtain the heat capacity. Our results show that the quasitopological Lifshitz dilaton black brane solutions are thermally stable for each positive value of the dynamical critiacl exponent, z.