AdS and Lifshitz black hole solutions in conformal gravity sourced with a scalar field

Abstract

In this paper we obtain exact asymptotically anti-de Sitter black hole solutions and asymptotically Lifshitz black hole solutions with dynamical exponents $z=0$ and $z=4$ of four-dimensional conformal gravity coupled with a self-interacting conformally invariant scalar field. Then, we compute their thermodynamical quantities, such as the mass, the Wald entropy and the Hawking temperature. The mass expression is obtained by using the generalized off-shell Noether potential formulation. It is found that the anti-de Sitter black holes as well as the Lifshitz black holes with $z=0$ have zero mass and zero entropy, although they have non-zero temperature. A similar behavior has been observed in previous works, where the integration constant is not associated with a conserved charge, and it can be interpreted as a kind of gravitational hair. On the other hand, the Lifshitz black holes with dynamical exponent $z=4$ have non-zero conserved charges, and the first law of black hole thermodynamics holds. Also, we analyze the horizon thermodynamics for the Lifshitz black holes with $z=4$, and we show that the first law of black hole thermodynamics arises from the field equations evaluated on the horizon. Furthermore, we study the propagation of a conformally coupled scalar field on these backgrounds and we find the quasinormal modes analytically in several cases. We find that for anti-de Sitter black holes and Lifshitz black holes with $z=4$, there is a continuous spectrum of frequencies for Dirichlet boundary condition; however, we show that discrete sets of well defined quasinormal frequencies can be obtained by considering Neumann boundary conditions.

References in corpus (17)

• Building an AdS/CFT superconductor
• The physical interpretation of the spectrum of black hole quasinormal modes
• Black hole mass and angular momentum in topologically massive gravity
• AdS and Lifshitz Black Holes in Conformal and Einstein-Weyl Gravities
• From conformal to Einstein Gravity
• Quasi Normal Modes for New Type Black Holes in New Massive Gravity
• Scalar field perturbations in asymptotically Lifshitz black holes
• Black holes in New Massive Gravity dressed by a (non)minimally coupled scalar field
• Static spherically symmetric solutions for conformal gravity in three dimensions
• On the thermodynamics of Lifshitz black holes
• Conserved Killing charges of quadratic curvature gravity theories in arbitrary backgrounds
• Conserved charges of black holes in Weyl and Einstein-Gauss-Bonnet gravities
• Charged Cylindrical Black Holes in Conformal Gravity
• Electromagnetic quasinormal modes of an asymptotically Lifshitz black hole
• Scalar field scattering by a Lifshitz black hole under a non-minimal coupling
• Fermionic field perturbations of a three-dimensional Lifshitz black hole in conformal gravity
• Quasinormal frequencies of the Dirac field in a D-dimensional Lifshitz black hole

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• Microscopic entropy of higher-dimensional nonminimally dressed Lifshitz black holes
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• Thermodynamics and Cardy-like formula for nonminimally dressed, charged Lifshitz black holes in New Massive Gravity
• Conformal renormalization of scalar-tensor theories
• Black hole solutions in modified gravity induced by quantum metric fluctuations
• Stationary Lifshitz Black Hole of New Massive Gravity
• Mass and angular momentum of charged rotating Gödel black holes in five-dimensional minimal supergravity
• Scalar Clouds and Quasinormal Modes