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Article
Report number	arXiv:2203.05589 ; CERN-TH-2022-038
Title	Generalized quasi-topological gravities: the whole shebang
Author(s)	Bueno, Pablo (CERN) ; Cano, Pablo A. (Leuven U.) ; Hennigar, Robie A. (ICC, Barcelona U.) ; Lu, Mengqi (Waterloo U.) ; Moreno, Javier (Leuven U. ; Valparaiso U., Catolica)
Publication	2022-12-05
Imprint	2022-03-10
Number of pages	33
Note	33 pages
In:	Class. Quantum Gravity 40 (2023) 015004
DOI	10.1088/1361-6382/aca236 (publication)
Subject category	gr-qc ; General Relativity and Cosmology ; hep-th ; Particle Physics - Theory
Abstract	Generalized quasi-topological gravities (GQTGs) are higher-curvature extensions of Einstein gravity in $D$-dimensions. Their defining properties include possessing second-order linearized equations of motion around maximally symmetric backgrounds as well as non-hairy generalizations of Schwarzschild's black hole characterized by a single function, $f(r)\equiv - g_{tt}=g_{rr}^{-1}$, which satisfies a second-order differential equation. In arXiv:1909.07983 GQTGs were shown to exist at all orders in curvature and for general $D$. In this paper we prove that, in fact, $n-1$ inequivalent classes of order-$n$ GQTGs exist for $D\geq 5$. Amongst these, we show that one -- and only one -- type of densities is of the Quasi-topological kind, namely, such that the equation for $f(r)$ is algebraic. Our arguments do not work for $D=4$, in which case there seems to be a single unique GQT density at each order which is not of the Quasi-topological kind. We compute the thermodynamic charges of the most general $D$-dimensional order-$n$ GQTG, verify that they satisfy the first law and provide evidence that they can be entirely written in terms of the embedding function which determines the maximally symmetric vacua of the theory.
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