Quintessential quartic quasi-topological quartet

Abstract

Abstract:We construct the quartic version of generalized quasi-topological gravity, which was recently constructed to cubic order in arXiv:1703.01631. This class of theories includes Lovelock gravity and a known form of quartic quasi-topological gravity as special cases and possess a number of remarkable properties: (i) In vacuum, or in the presence of suitable matter, there is a single independent field equation which is a total derivative.(ii) At the linearized level, the equations of motion on a maximally symmetric background are second order, coinciding with the linearized Einstein equations up to a redefinition of Newton's constant. Therefore, these theories propagate only the massless, transverse graviton on a maximally symmetric background. (iii) While the Lovelock and quasi-topological terms are trivial in four dimensions, there exist four new generalized quasi-topological terms (the quartet) that are nontrivial, leading to interesting higher curvature theories in d ≥ 4 dimensions that appear well suited for holographic study. We construct four dimensional black hole solutions to the theory and study their properties. A study of black brane solutions in arbitrary dimensions reveals that these solutions are modified from the 'universal' properties they possess in other higher curvature theories, which may lead to interesting consequences for the dual CFTs.

(Generalized) quasi-topological gravities at all orders

“…Now, examples of GQTGs have been constructed in general dimensions and for considerably high orders of curvature [4][5][6][7][8][9][10]23]. Analyzing the existent cases, we observe that all of them satisfy the total derivative condition (9) with…”

“…GQTG densities possess a series of interesting properties which have been studied in many papers and appear summarized in some detail e.g., in [1]. Among the most relevant ones, we can mention: i) when linearized around any maximally symmetric background, their equations are identical to the Einstein gravity ones, up to a redefinition of the Newton constant -in other words, they only propagate the usual transverse and traceless graviton in the vacuum [4][5][6][7][8][9][10]; 2 ii) they possess non-hairy black hole solutions fully characterized by their ADM mass/energy and whose thermodynamic properties can be obtained from an algebraic system of equations; iii) at least in D = 4, black holes generically become thermodynamically stable below certain mass [10]; iv) in addition to black holes, certain subsets of GQTGs also contain Taub-NUT/Bolt solutions characterized by a single metric function and analytic thermodynamics [17]; v) when evaluated on a Friedmann-Lemaître-Robertson-Walker (FLRW) ansatz, certain GQTGs in D = 4 also give rise to second-order equations for the scale factor, with intriguing consequences regarding cosmological evolution [21][22][23]; vi) we can consider arbitrary linear combinations of GQTG densities and the corresponding properties hold, which means, in particular, that GQTG theories have a well-defined and continuous Einstein gravity limit, corresponding to setting all higher-curvature couplings to zero.…”

“…Theories of this subclass only exist for D ≥ 5. Prior to this paper, Quasi-topological gravities had been constructed order by order in curvature for n = 3 [39,40], n = 4 [9,45] and n = 5 in D = 5 [44]. A particular subclass of Quasi-topological gravities -characterized by the additional property that the trace of the field equations is second-order in derivatives of the metric for general backgrounds-had been previously identified in D = 2n − 1 for general n [39,42,46].…”

Partition functions on slightly squashed spheres and flux parameters

“…are two canonically-normalized quartic GQT densities [65]. In particular, Z belongs to the QT subfamily, as it modifies the equation of f (r) for static black holes algebraically.…”

Extremal rotating black holes in Einsteinian cubic gravity

“…Plugging this expansion together with (34) in the equation (25) we find the equation satisfied by every component g k (y). The leading term g 0 -which is the only one that survives in the limit x 0 → 0 -satisfies the following equation…”