Journal of High Energy Physics

, 2019:62 | Cite as

All higher-curvature gravities as Generalized quasi-topological gravities

  • Pablo Bueno
  • Pablo A. Cano
  • Javier Moreno
  • Ángel MurciaEmail author
Open Access
Regular Article - Theoretical Physics


Generalized quasi-topological gravities (GQTGs) are higher-curvature extensions of Einstein gravity characterized by the existence of non-hairy generalizations of the Schwarzschild black hole which satisfy gttgrr = –1, as well as for having second-order linearized equations around maximally symmetric backgrounds. In this paper we provide strong evidence that any gravitational effective action involving higher-curvature corrections is equivalent, via metric redefinitions, to some GQTG. In the case of theories involving invariants constructed from contractions of the Riemann tensor and the metric, we show this claim to be true as long as (at least) one non-trivial GQTG invariant exists at each order in curvature-and extremely conclusive evidence suggests this is the case in general dimensions. When covariant derivatives of the Riemann tensor are included, the evidence provided is not as definitive, but we still prove the claim explicitly for all theories including up to eight derivatives of the metric as well as for terms involving arbitrary contractions of two covariant derivatives of the Riemann tensor and any number of Riemann tensors. Our results suggest that the physics of generic higher-curvature gravity black holes is captured by their GQTG counterparts, dramatically easier to characterize and universal. As an example, we map the gravity sector of the Type-IIB string theory effective action in AdS5 at order 𝒪 (α3) to a GQTG and show that the thermodynamic properties of black holes in both frames match.


Classical Theories of Gravity Black Holes Black Holes in String Theory 


Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Instituto Balseiro, Centro Atómico BarilocheRío NegroArgentina
  2. 2.Instituto de Física Teórica UAM/CSICMadridSpain
  3. 3.Instituto de FísicaPontificia Universidad Católica de ValparaísoValparaísoChile

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