On the classification of Generalized Quasitopological Gravities

Javier Moreno; Ángel J. Murcia

doi:10.1103/PhysRevD.108.044016

paper

On the classification of Generalized Quasitopological Gravities

arXiv:2304.08510 · doi:10.1103/PhysRevD.108.044016

Abstract

Generalized Quasitopological Gravities (GQTGs) are higher-order extensions of Einstein gravity in $D$ dimensions satisfying a number of interesting properties, such as possessing second-order linearized equations of motion on top of maximally symmetric backgrounds, admitting non-hairy generalizations of the Schwarzschild-Tangherlini black hole which are characterized by a single metric function or forming a perturbative spanning set of the space of effective theories of gravity. In this work, we classify all inequivalent GQTGs at all curvature orders $n$ and spacetime dimension $D \geq 4$ . This is achieved after the explicit construction of a dictionary that allows the uplift of expressions evaluated on a single-function static and spherically symmetric ansatz into fully covariant ones. On the one hand, applying such prescription for $D \geq 5$ , we find the explicit covariant form of the unique inequivalent Quasitopological Gravity that exists at each $n$ and, for the first time, the covariant expressions of the $n - 2$ inequivalent proper GQTGs existing at every curvature order $n$ . On the other hand, for $D = 4$ , we are able to provide the first rigorous proof of the fact that there is one and only one (proper) inequivalent GQTG at each curvature order $n$ , deriving along the way a simple expression for such four-dimensional representative at every order $n$ .

arXiv comment42 pages, 2 appendices, no figures

On the classification of Generalized Quasitopological Gravities

Abstract

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