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Generalized quasi-topological gravities: the whole shebang
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Generalized quasi-topological gravities: the whole shebang
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Generalized quasi-topological gravities (GQTGs) are higher-curvature extensions of Einstein gravity in $D$-dimensions. Their defining properties include possessing second-order linearized equations of motion around maximally symmetric backgrounds as well as non-hairy generalizations of Schwarzschild's black hole characterized by a single function, $f(r)\equiv - g_{tt}=g_{rr}^{-1}$, which satisfies a second-order differential equation. In arXiv:1909.07983 GQTGs were shown to exist at all orders in curvature and for general $D$. In this paper we prove that, in fact, $n-1$ inequivalent classes of order-$n$ GQTGs exist for $D\geq 5$. Amongst these, we show that one -- and only one -- type of densities is of the Quasi-topological kind, namely, such that the equation for $f(r)$ is algebraic. Our arguments do not work for $D=4$, in which case there seems to be a single unique GQT density at each order which is not of the Quasi-topological kind. We compute the thermodynamic charges of the most general $D$-dimensional order-$n$ GQTG, verify that they satisfy the first law and provide evidence that they can be entirely written in terms of the embedding function which determines the maximally symmetric vacua of the theory.
Forward citations
Cited by 12 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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$g_{tt}g_{rr} =-1$ 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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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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