<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math>-dimensional log gravity

Alishahiha, Mohsen; Fareghbal, Reza

doi:10.1103/physrevd.83.084052

Cited by 72 publications

(112 citation statements)

References 33 publications

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“…Then, taking the metric to be in the Kundt subclass of type-N spacetimes we show that AdS-plane wave [7,8] and AdS-spherical wave [9] solutions of the quadratic gravity theory are also the solutions of the f R µν ρσ theory. Log terms arising in the solutions of the quadratic gravity exist also in some f R µν ρσ theories corresponding to the generalizations of critical gravity [10,11].…”

Section: Pacs Numbersmentioning

confidence: 99%

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Anti–de Sitter–Wave Solutions of Higher Derivative Theories

et al. 2013

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We show that the recently found AdS-plane and AdS-spherical wave solutions of quadratic curvature gravity also solve the most general higher derivative theory in D-dimensions. More generally, we show that the field equations of such theories reduce to an equation linear in the Ricci tensor for Kerr-Schild spacetimes having type-N Weyl and traceless Ricci tensors. PACS numbers:There is a vast literature on the exact solutions of fourdimensional Einstein's gravity. But, as more powers of curvature are added, or computed in a microscopic theory such as string theory, to get a better UV behaved theory, the field equations become highly nontrivial and so solutions are not easy to find. In fact, only a few classes of solutions are known: For example, see [1][2][3][4] for solutions in low energy string theory. AdS 5 × S 5 , which played a major role in AdS/CFT, is also expected to be an exact solution of string theory [5]. In this work, we present new asymptotically AdS solutions, which are AdS-plane and AdS-spherical waves, to D-dimensional generic gravity theories based on the Riemann tensor and its arbitrary number of covariant derivatives which are in some sense natural geometric extensions of Einstein's gravity. Certain low energy string theory actions constitute a subclass of this theory once all the non-gravitational fields are turned off [6]. Asymptotically AdS solutions in higher derivative theories are relevant in the context of generic gravity/gauge theory dualities and holography. Here, we shall provide such solutions.Using a theorem given in [4], we first prove that any spacetime with type-N Weyl and traceless Ricci tensors, where the metric is the Kerr-Schild form, the field equations of the most general higher derivative theory reduce to a linear equation for the traceless Ricci tensor. These spacetimes have constant scalar invariants. Furthermore, using the the type-N property of the traceless Ricci tensor in these field equations, we obtain a linear partial differential equation for the metric function V of order 2N in the AdS background, where N is related to the number of covariant derivatives in the action of the theory. This result implies that the AdS-wave metrics are universal in the sense defined in [4].As a special case, the field equations of the theory * Electronic address: gurses@fen.bilkent.edu.tr † Electronic address: sigbjorn.hervik@uis.no ‡ Electronic address: tahsin.c.sisman@gmail.com § Electronic address: btekin@metu.edu.tr which depends on the contractions of the Riemann tensor but not on its derivatives, f R µν ρσ theory, arealso highly cumbersome, but using our general result for type-N spacetimes under certain assumptions they reduce to those of the quadratic gravity. Then, taking the metric to be in the Kundt subclass of type-N spacetimes we show that AdS-plane wave [7,8] and AdS-spherical wave [9] solutions of the quadratic gravity theory are also the solutions of the f R µν ρσ theory. Log terms arising in the solutions of the quadratic gravity exist also in some f R µν ρσ theori...

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Section: Pacs Numbersmentioning

confidence: 99%

“…But, we know at least two solutions which are the AdS-plane [7,8] and the AdS-spherical waves [9]. These waves are of the Kerr-Schild form, g µν =ḡ µν + 2V ℓ µ ℓ ν , which belong to the Kundt class of type-N spacetimes [19,20].…”

Section: Type-n Weyl and Traceless Ricci Tensorsmentioning

confidence: 99%

Anti–de Sitter–Wave Solutions of Higher Derivative Theories

et al. 2013

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“…However, it was discussed in the 4D quadratic curvature gravity [6] that at the critical point, the AdS-wave log solutions may provide a dual LCFT 3 , while at off-critical point, its dual theory may correspond to a nonrelativistic field theory with fixed boundary conditions.…”

Section: Discussionmentioning

confidence: 99%

“…To that end, critical gravities have received much attention because they were considered as toy models for quantum gravity [2,3,4,5,6,7,8]. At the critical point, a degeneracy takes place in the AdS spacetimes and thus, ghost-like massive gravitons become massless gravitons.…”

Section: Introductionmentioning

confidence: 99%

Tricritical gravity waves in the four-dimensional generalized massive gravity

Moon

Myung

2013

Eur. Phys. J. C

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We construct a generalized massive gravity by combining quadratic curvature gravity with the Chern-Simons term in four dimensions. This may be a candidate for the parity-odd tricritical gravity theory. Considering the AdS 4 vacuum solution, we derive the linearized Einstein equation, which is not similar to that of the three dimensional (3D) generalized massive gravity. When a perturbed metric tensor is chosen to be the Kerr-Schild form, the linearized equation reduces to a single massive scalar equation. At the tricritical points where two masses are equal to −1 and 2, we obtain a log-square wave solution to the massive scalar equation. This is compared to the 3D tricritical generalized massive gravity whose dual is a rank-3 logarithmic conformal field theory.

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“…To this end, we would like to comment that the critical gravities as candidates for quantum gravity were recently investigated in the AdS spacetimes [2,3,4,5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Critical gravity in the Chern–Simons modified gravity

Moon

Myung

2011

Eur. Phys. J. C

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We perform the perturbation analysis of the Chern-Simons modified gravity around the AdS 4 spacetimes (its curvature radius ℓ) to obtain the critical gravity. In general, we could not obtain an explicit form of perturbed Einstein equation which shows a massive graviton propagation clearly, but for the Kerr-Schild perturbation and Chern-Simons coupling θ = kx/y, we find the AdS wave as a single massive solution to the perturbed Einstein equation. Its mass squared is given by M 2 = [−9 + (2ℓ 2 /k − 1) 2 ]/4ℓ 2 . At the critical point of M 2 = 0(k = ℓ 2 /2), the solution takes the log-form and the linearized excitation energies vanish.

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D-dimensional log gravity

Cited by 72 publications

References 33 publications

Anti–de Sitter–Wave Solutions of Higher Derivative Theories

Anti–de Sitter–Wave Solutions of Higher Derivative Theories

Tricritical gravity waves in the four-dimensional generalized massive gravity

Critical gravity in the Chern–Simons modified gravity

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