Quintic quasi-topological gravity

Abstract

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.

Partition functions on slightly squashed spheres and flux parameters

“…where here χ h ≡ f (r h ) = −L 2 k/r 2 h . These expressions properly reduce to the previously known ones corresponding to: n = 3 for general d [71,72], n = 4 for general d [65,73], and n = 5 in d = 4 [74].…”

“…Until recently, no additional AdS-Taub-NUT solutions were known in d+1 = 4 bulk dimensions for any other metric theories of gravity. However, new solutions of that kind have been recently constructed in [60] for cubic and quartic higher-order gravities of the so-called Generalized Quasi-topological (GQT) class [61][62][63][64][65][66][67][68][69][70][71][72][73][74]. Remarkably, the thermodynamic properties of such solutions can be obtained fully analytically -and nonperturbatively in the higher-order couplings-in all cases.…”

“…As we have emphasized before, the equations of motion of QT theories evaluated on static black hole solutions with various horizon topologies are algebraic for the metric function, and particularly simple [65,[71][72][73][74]. In particular, consider a general (d + 1)-dimensional QT action of the form…”

Generalized quasitopological gravity

“…The inclusion of quadratic terms has been shown to lead to violations of the Kovtun-SonStarinets (KSS) viscosity/entropy ratio bound [9,10]. Holography has even motivated the construction of new higher curvature gravities, such as quasi-topological gravity [11][12][13][14][15][16].…”

Black holes and solitons in an extended Proca theory

“…Recently there was some activity finding hairy solutions for the above theory [41,43,44]. For the case µ = 0 the case of a particular coupling β = 1/4 was studied [41].…”