Energy in generic higher curvature gravity theories

We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing R 5 terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes. These theories have recently received attention since when formulated on asymptotically AdS spacetimes might provide for gravity duals of a broad class of CFTs. For simplicity we focus on five dimensions. We show that this theory fulfils a Birkhoff's Theorem as it is the case in Lovelock gravity and therefore, for generic values of the couplings, there is no s-wave propagating mode. We prove that the spherically symmetric solution is determined by a quintic algebraic polynomial equation which resembles Wheeler's polynomial of Lovelock gravity. For the black hole solutions we compute the temperature, mass and entropy and show that the first law of black holes thermodynamics is fulfilled. Besides of being of fourth order in general, we show that the field equations, when linearized around AdS are of second order, and therefore the theory does not propagate ghosts around this background. Besides the class of theories originally introduced in arXiv:1003.4773, the general geometric structure of these Lagrangians remains an open problem.

Section: Jhep04(2017)066mentioning

confidence: 99%

Quintic quasi-topological gravity

Cisterna

Guajardo

Hassaı̈ne

et al. 2017

“…Given that the Kaluza-Klein reduction which yielded the dilatonic solution is diagonal, it is straightforward to derive all thermodynamic quantities in the lower-dimensional frame from the known higher-dimensional ones, [76,112,113,120,[126][127][128]. Note that the latter may be recovered by setting δ = 0 in all subsequent formulae, obtaining the thermodynamics of the pure Gauss-Bonnet black hole in p + 1 dimensions.…”

Section: Thermodynamicsmentioning

confidence: 99%

Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography

Charmousis

Goutéraux

Kiritsis

2012

We consider a general Kaluza-Klein reduction of a truncated Lovelock theory. We find necessary geometric conditions for the reduction to be consistent. The resulting lower-dimensional theory is a higher derivative scalar-tensor theory, depends on a single real parameter and yields second-order field equations. Due to the presence of higherderivative terms, the theory has multiple applications in modifications of Einstein gravity (Galileon/Horndesky theory) and holography (Einstein-Maxwell-Dilaton theories). We find and analyze charged black hole solutions with planar or curved horizons, both in the 'Einstein' and 'Galileon' frame, with or without cosmological constant. Naked singularities are dressed by a geometric event horizon originating from the higher-derivative terms. The near-horizon region of the near-extremal black hole is unaffected by the presence of the higher derivatives, whether scale invariant or hyperscaling violating. In the latter case, the area law for the entanglement entropy is violated logarithmically, as expected in the presence of a Fermi surface. For negative cosmological constant and planar horizons, thermodynamics and first-order hydrodynamics are derived: the shear viscosity to entropy density ratio does not depend on temperature, as expected from the higher-dimensional scale invariance.

“…We will also extend these results to the case of charged planar black holes, where again the ground state is identified with the soliton derived from the neutral and nonrotating black hole. Since the soliton is devoid of any integration constant, its mass will be computed using the quasilocal generalization of the ADT formalism [22][23][24][25][26] as presented in refs. [27,28].…”

Section: Jhep04(2017)092mentioning

confidence: 99%

A Cardy-like formula for rotating black holes with planar horizon

Bravo‐Gaete

Guajardo

2017

We show that the semiclassical entropy of D−dimensional rotating (an)isotropic black holes with planar horizon can be successfully computed according to a Cardy-like formula. This formula does not refer to any central charges but instead involves the vacuum energy which is identified with a gravitational bulk soliton. The soliton is obtained from the non-rotating black hole solution by means of a double analytic continuation. The robustness of the Cardy-like formula is tested with numerous and varied examples, including AdS, Lifshitz and hyperscaling violation planar black holes.