# All higher-curvature gravities as Generalized quasi-topological gravities

## TL;DR

This paper demonstrates that all higher-curvature gravity theories can be reformulated as Generalized quasi-topological gravities (GQTGs), simplifying the analysis of black hole solutions and their thermodynamics across various theories.

## Contribution

It proves that higher-curvature effective actions are equivalent to GQTGs via metric redefinitions, unifying the description of black holes in these theories.

## Key findings

- Any higher-curvature gravity theory can be mapped to a GQTG.
- Black hole thermodynamics in higher-curvature theories matches that of GQTGs.
- The mapping applies to string theory effective actions at order (\u03b1'^{3}) in AdS$_5$.

## Abstract

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 $g_{tt}g_{rr}=-1$, 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 AdS$_5$ at order $\mathcal{O}({\alpha^{\prime}}^3)$ to a GQTG and show that the thermodynamic properties of black holes in both frames match.