Generalized quasitopological gravity

Abstract

We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possess the following remarkable properties: i) it has a well-defined Einstein gravity limit ii) it admits 'Schwarzschild-like' solutions characterized by a single metric function iii) on maximally symmetric backgrounds it propagates the same degrees of freedom as Einstein's gravity iv) Lovelock and quasi-topological gravities, as well as the recently developed Einsteinian cubic gravity ArXiv:1607.06463 in four dimensions, are recovered as special cases. We perform a brief analysis of asymptotically flat black holes in this theory and study their thermodynamics.

(Generalized) quasi-topological gravities at all orders

“…GQTG densities have been previously constructed for: n = 3 and general D ≥ 4 in [7]; n = 4 and general D ≥ 4 in [9]; n = 5, · · · , 10 and D = 4 in [10,23]. Here we extend those results to general n and D ≥ 4.…”

“…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.…”

Partition functions on slightly squashed spheres and flux parameters

“…Let us now restrict ourselves to GQT theories. Their defining property is the following [64,69,70]. Consider a general static and spherically symmetric metric of the form 19) and let L N,V ≡ √ −gL| N,V be the effective Lagrangian resulting from the evaluation of L on (2.19).…”

Higher order gravities and the Strong Equivalence Principle

“…refs. [21][22][23][24][25][26][27][28][29][30][31][32][33]) and in the study of spacetime singularities.…”