(Generalized) quasitopological gravities at all orders
Abstract
A new class of highercurvature modifications of [ image ])dimensional Einstein gravity has been recently identified. Densities belonging to this 'Generalized quasitopological' class (GQTGs) are characterized by possessing nonhairy generalizations of the Schwarzschild black hole satisfying [ image ] and by having secondorder equations of motion when linearized around maximally symmetric backgrounds. GQTGs for which the equation of the metric function [ image ] is algebraic are called 'Quasitopological' and only exist for [ image ]. In this paper we prove that GQTG and Quasitopological densities exist in general dimensions and at arbitrarily high curvature orders. We present recursive formulas which allow for the systematic construction of nth order densities of both types from lower order ones, as well as explicit expressions valid at any order. We also obtain the equation satisfied by [ image ] for general D and n. Our results here tie up the remaining loose end in the proof presented in Bueno et al (2019 (arXiv:1906.00987)) that every gravitational effective action constructed from arbitrary contractions of the metric and the Riemann tensor is equivalent, through a metric redefinition, to some GQTG.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 January 2020
 DOI:
 10.1088/13616382/ab5410
 arXiv:
 arXiv:1909.07983
 Bibcode:
 2020CQGra..37a5002B
 Keywords:

 black holes;
 higherorder gravities;
 gravitational effective actions;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 27 pages