Lifshitz black holes in four-dimensional critical gravity

In this work, we study the existence of asymptotically Lifshitz black holes in critical gravity in four dimensions with a negative cosmological constant under two scenarios: First, including dilatonic fields as the matter source, where we find an asymptotically Lifshitz solution for a fixed value of the dynamical exponent z = 4. As a second case, we also added a nonminimally coupled scalar field Phi with a potential given by a mass term and a quartic term. Using this approach, we found a solution for z defined in the interval (1,4), recovering the Schwarzchild-anti-de Sitter case with planar base manifold in the isotropic limit. Moreover, when we analyzed the limiting case z = 4, we found that there exists an additional solution that can be interpreted as a stealth configuration in which the stealth field is overflying the z = 4 solution without the nonminimally coupled field Phi. Finally, we studied the nontrivial thermodynamics of these new anisotropic solutions and found that they all satisfy the first law of thermodynamics as well as the Smarr relation. We were also able to determine that the nonstealth configuration is thermodynamically preferred in this case.

Automated summary

In this work, we study the existence of asymptotically Lifshitz black holes in four dimensions with a negative cosmological constant. We consider two scenarios, including dilatonic fields and a nonminimally coupled scalar field. We find solutions for specific values of the dynamical exponent, as well as additional solutions in the limiting case. We also study the thermodynamics of these new solutions and find that they satisfy the first law of thermodynamics and the Smarr relation.