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All higher-curvature gravities as Generalized quasi-topological gravities
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All higher-curvature gravities as Generalized quasi-topological gravities
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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.
Forward citations
Cited by 14 Pith papers
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Regular Black Holes in Nonlocal Quasitopological Gravity
Infinite-derivative completions of quasitopological gravities are ghost-free, avoid strong coupling, and admit exact spherically symmetric vacuum regular black holes obeying a perturbative Birkhoff theorem.
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Quasi-topological gravity for 4-dimensional Taub-NUT, near-horizon extreme Kerr, and swirling symmetries
Unique quasi-topological theories with first-order equations are found for Taub-NUT, NHEK, swirling and related 4D symmetric metrics, enabling closed-form solutions and regular black holes from high-order curvature co...
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Cosmologically viable non-polynomial quasi-topological gravity: explicit models, $\Lambda$CDM limit and observational constraints
Non-polynomial quasi-topological gravity models reproduce the standard thermal history, generate dynamical dark energy of geometric origin, and fit supernova, cosmic chronometer, and BAO data competitively with ΛCDM.
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Cosmic Inflation From Regular Black Holes
Regular black holes in the bulk of quasi-topological gravity drive a de Sitter inflationary phase on the brane at small scales, with e-fold number set by the ratio of black hole radius to higher-curvature scale.
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All $2D$ generalised dilaton theories from $d\geq 4$ gravities
Generic 2D Horndeski theories arise from dimensional reduction of d≥4 gravities, yielding a Birkhoff theorem for quasi-topological gravities where static spherically symmetric solutions satisfy g_tt g_rr = -1 and are ...
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Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry
RG-improved black hole spacetimes with scale-dependent gravitational coupling are derived as vacuum solutions to 2D Horndeski master field equations, embedding prior works and exposing implementation discrepancies.
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Cosmological higher-curvature gravities
Higher-curvature gravities are constructed in which both FLRW backgrounds and linearized scalar perturbations obey at most second-order differential equations.
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$g_{tt}g_{rr} =-1$ black hole thermodynamics in extended quasi-topological gravity
A unified framework links the generating function for static black holes satisfying g_tt g_rr=-1 in extended quasi-topological gravity to thermodynamic mass and Wald entropy via an effective 2D dilaton theory.
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$O(d,d)$ symmetric gravity and finite coupling holography
In O(d,d) symmetric gravity with curvature corrections, black brane singularities persist with altered Kasner exponents, while dilaton effects enable dynamic generation of negative cosmological constants at weak coupling.
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Charged Black Holes in Quasi-Topological Gravity Coupled to Born-Infeld Nonlinear Electrodynamics
Derives exact charged black hole solutions in quasi-topological gravity with Born-Infeld electrodynamics, showing model-dependent regularity with some cases having finite-radius singularities and others replacing de S...
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Charged Black Holes in Quasi-Topological Gravity Coupled to Born-Infeld Nonlinear Electrodynamics
Exact charged black hole solutions in quasi-topological gravity with Born-Infeld electrodynamics are constructed, revealing model-dependent interior regularity with some cases singular and others regular but with AdS cores.
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Regular Black Holes in Quasitopological Gravity: Null Shells and Mass Inflation
Significant mass inflation in quasitopological regular black holes requires null shell collisions at radial separations r-r_* ≲ ℓ(ℓ/r_g)^{2n(D-3)} from the inner horizon.
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$O(d,d)$ symmetric gravity and finite coupling holography
In O(d,d) symmetric gravity with curvature corrections, black brane singularities are not resolved but approach with altered Kasner exponents, while a dilaton generates negative cosmological constants at small coupling.
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From Ringdown to Lensing: Analytic Eikonal Modes of Quasi-Topological Regular Black Holes
Analytic quasinormal-mode expressions and explicit QNM-shadow-lensing correspondence for four-dimensional quasi-topological regular black holes.
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