New exact solutions of quadratic curvature gravity

Gürses, Metin; Şişman, Tahsin Çağrı; Tekin, Bayram

doi:10.1103/physrevd.86.024009

Cited by 46 publications

(78 citation statements)

References 52 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%

“…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%

“…Solutions of such linear partial differential equations are given in [7] and [9] in the of AdS background. As a conclusion we can say that the AdS-wave metrics found recently [7] and [9] solve the field equations of the most general higher derivative theories.…”

Section: Type-n Weyl and Traceless Ricci Tensorsmentioning

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%

Section: Type-n Weyl and Traceless Ricci Tensorsmentioning

confidence: 99%

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Anti–de Sitter–Wave Solutions of Higher Derivative Theories

et al. 2013

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“…Ayòn-Beato et al studied the Ads-wave solutions to NMG [13]. More recently, Gürses et al [14][15][16][17] also studied solutions to general three-dimensional gravitational models in an exhaustive manner.…”

Section: Introductionmentioning

confidence: 99%

“…(14) together with Eqs. (15)(16)(17) can be used to write out the TMG equations using the spinorial components given in scalar form in, e.g. Ref.…”

Section: Geometrical Preliminarymentioning

confidence: 99%

Impulsive gravitational waves in general massive 3D gravity

Baykal

Dereli

2017

Phys. Rev. D

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Instability of BTZ black holes in parity-even massive gravity

Jafari

Soltanpanahi

2019

J. High Energ. Phys.

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We investigate the linearized equations of motion in three dimensional Born-Infeld gravity theory. Motivated by this model, we calculate the quasinormal modes of BTZ black hole solutions of parity-even gravity theories in three dimensions by using numerical methods. The results are classified in three families and they are so accurate such that it allows us to propose analytical form for the quasinormal frequencies. We find new quasinormal modes which have been missing in the literature of the analytical studies of three dimensional massive gravitons. These new modes do not have the known tower structure and they are purely imaginary for any value of the angular momenta. Considering the complete set of the quasinormal modes, we show that the BTZ black hole solutions are unstable for any value of the parameters of the theory. We confirm our numerical results by computing the new eigenmodes analytically at zero angular momentum.

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New exact solutions of quadratic curvature gravity

Cited by 46 publications

References 52 publications

Anti–de Sitter–Wave Solutions of Higher Derivative Theories

Anti–de Sitter–Wave Solutions of Higher Derivative Theories

Impulsive gravitational waves in general massive 3D gravity

Instability of BTZ black holes in parity-even massive gravity

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