A new cubic theory of gravity in five dimensions: black hole, Birkhoff's theorem and
                    <i>C</i>
                    -function

Oliva, Julio; Ray, Sourya

doi:10.1088/0264-9381/27/22/225002

Cited by 212 publications

(317 citation statements)

References 58 publications

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“…Nevertheless, continuing the solution (7.4) to D = 5 and k = 5, correctly reproduces the line element (7.2). For cubic quasi-topological gravity, this property was already pointed out in [7].…”

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confidence: 66%

“…1 It was also realized in [7] that this theory belongs to a general family of Lagrangians of order k in the curvature, that can be constructed in dimensions D = 2k − 1 for k ≥ 3, and have the simple form…”

Section: Jhep04(2017)066mentioning

confidence: 99%

“…As mentioned above, besides the clear structure provided by the family of theories introduced in [7], of order k in dimension D = 2k − 1, the general form of quasi-topological gravities of arbitrary high order in five dimensions, is not clear. For the quartic case for example, one might be tempted to consider combinations of the invariants: Substituting the Weyl tensor in terms of the Riemann tensor and its traces, one can see that the combination Then, in order to remove the higher derivative contributions to the field equations one would have to engineer additional terms that on spherical symmetry contribute as those in the combinations that appear in B.…”

Section: Jhep04(2017)066mentioning

confidence: 99%

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Quintic quasi-topological gravity

Cisterna

Guajardo

Hassaı̈ne

et al. 2017

J. High Energ. Phys.

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We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing R 5 terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes. These theories have recently received attention since when formulated on asymptotically AdS spacetimes might provide for gravity duals of a broad class of CFTs. For simplicity we focus on five dimensions. We show that this theory fulfils a Birkhoff's Theorem as it is the case in Lovelock gravity and therefore, for generic values of the couplings, there is no s-wave propagating mode. We prove that the spherically symmetric solution is determined by a quintic algebraic polynomial equation which resembles Wheeler's polynomial of Lovelock gravity. For the black hole solutions we compute the temperature, mass and entropy and show that the first law of black holes thermodynamics is fulfilled. Besides of being of fourth order in general, we show that the field equations, when linearized around AdS are of second order, and therefore the theory does not propagate ghosts around this background. Besides the class of theories originally introduced in arXiv:1003.4773, the general geometric structure of these Lagrangians remains an open problem.

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confidence: 66%

Section: Jhep04(2017)066mentioning

confidence: 99%

Section: Jhep04(2017)066mentioning

confidence: 99%

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Quintic quasi-topological gravity

Cisterna

Guajardo

Hassaı̈ne

et al. 2017

J. High Energ. Phys.

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“…Of crucial interest is, of course, the existence and, if this is the case, the properties of black holes in modified gravities. It is quite easy to find the conditions allowing the existence of de Sitter-Schwarzschild black holes (see, for example [22] for f (R) modified gravity, [23] for Gauss-Bonnet modified gravity, and [24][25][26][27] for related topics).…”

Section: Introductionmentioning

confidence: 99%

Black Hole Entropy for Two Higher Derivative Theories of Gravity

Bellini

Criscienzo

Sebastiani

et al. 2010

Entropy

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The dark energy issue is attracting the attention of an increasing number of physicists all over the world. Among the possible alternatives to explain what as been named the "Mystery of the Millennium" are the so-called Modified Theories of Gravity. A crucial test for such models is represented by the existence and (if this is the case) the properties of their black hole solutions. Nowadays, to our knowledge, only two non-trivial, static, spherically symmetric, solutions with vanishing cosmological constant are known by Barrow & Clifton (2005) and Deser, Sarioglu & Tekin (2008). The aim of the paper is to discuss some features of such solutions, with emphasis on their thermodynamic properties such as entropy and temperature.

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“…Therefore, in the setup we have considered, it is not possible to check the coefficient of t 4 in (1.4). In order to test the coefficient of t 4 , we need to incorporate cubic curvature corrections to the classical action as explored in [28][29][30]. The authors of [29] consider a specific combination of cubic curvature corrections to the Einstein Hilbert action such that the equations of motion are second order in derivatives and obtain exact black hole solutions in AdS background.…”

Section: Jhep12(2017)156mentioning

confidence: 99%

Shear sum rule in higher derivative gravity theories

Chowdhury

2017

J. High Energ. Phys.

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We study holographic shear sum rules in Einstein gravity with curvature squared corrections. Sum rules relate weighted integral over spectral densities of retarded correlators in the shear channel to the one point functions of the CFTs. The proportionality constant can be written in terms of the data of three point functions of the stress tensors of the CFT (t 2 and t 4 ). For CFTs dual to two derivative Einstein gravity, this proportionality constant is just d 2(d+1) . This has been verified by a direct holographic computation of the retarded correlator for Einstein gravity in AdS d+1 black hole background. We compute corrections to the holographic shear sum rule in presence of higher derivative corrections to the Einstein-Hilbert action. We find agreement between the sum rule obtained from a general CFT analysis and holographic computation for Gauss Bonnet theories in AdS 5 black hole background. We then generalize the sum rule for arbitrary curvature squared corrections to Einstein-Hilbert action in d ≥ 4. Evaluating the parameters t 2 and t 4 for the possible dual CFT in presence of such curvature corrections, we find an agreement with the general field theory derivation to leading order in coupling constants of the higher derivative terms.

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A new cubic theory of gravity in five dimensions: black hole, Birkhoff's theorem and C -function

Cited by 212 publications

References 58 publications

Quintic quasi-topological gravity

Quintic quasi-topological gravity

Black Hole Entropy for Two Higher Derivative Theories of Gravity

Shear sum rule in higher derivative gravity theories

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