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(Generalized) quasi-topological gravities at all orders
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(Generalized) quasi-topological gravities at all orders
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A new class of higher-curvature modifications of $D(\geq 4$)-dimensional Einstein gravity has been recently identified. Densities belonging to this "Generalized quasi-topological" class (GQTGs) are characterized by possessing non-hairy generalizations of the Schwarzschild black hole satisfying $g_{tt}g_{rr}=-1$ and by having second-order equations of motion when linearized around maximally symmetric backgrounds. GQTGs for which the equation of the metric function $f(r)\equiv -g_{tt}$ is algebraic are called "Quasi-topological" and only exist for $D\geq 5$. In this paper we prove that GQTG and Quasi-topological densities exist in general dimensions and at arbitrarily high curvature orders. We present recursive formulas which allow for the systematic construction of $n$-th 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 $f(r)$ for general $D$ and $n$. Our results here tie up the remaining loose end in the proof presented in 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.
Forward citations
Cited by 16 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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On mass inflation and thin shells in quasi-topological gravity
Regular black holes in quasi-topological gravity lack null thin shells in standard distributional theory, invalidating the usual mass inflation derivation and leaving inner horizon stability unresolved.
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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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Regular Vaidya solutions of effective gravitational theories
Regular Vaidya solutions exist in effective gravitational theories that dynamically describe radiation-driven formation of regular black holes or mimickers without curvature singularities.
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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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Charging up regular black holes
Charged Bardeen and Hayward metrics become singular under deformed Einstein–Maxwell equations; more stringent regularity conditions are derived and improved regular charged metrics are constructed.
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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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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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Scattering of electromagnetic field in quasi-topological gravity
Regular black holes in quasi-topological gravity produce shifted electromagnetic absorption spectra and modified photon sphere radii relative to singular Tangherlini solutions, with deviations suppressed as spacetime ...
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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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Grey-body factors of higher dimensional regular black holes in quasi-topological theories
Higher dimensional regular black holes in quasi-topological gravity have suppressed grey-body factors and Hawking radiation compared to singular black holes in general relativity.
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Grey-body factors of higher dimensional regular black holes in quasi-topological theories
Higher-dimensional regular black holes in quasi-topological gravity exhibit significantly suppressed grey-body factors and Hawking evaporation compared to singular black holes in general relativity.
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