Kundt spacetimes

Coley, A. A.; Hervik, Sigbjørn; Papadopoulos, Georgios; Pelavas, Nicos

doi:10.1088/0264-9381/26/10/105016

Cited by 130 publications

(217 citation statements)

References 37 publications

(133 reference statements)

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“…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]. Here,ḡ µν is the AdS background metric and the function V satisfies ℓ µ ∂ µ V = 0.…”

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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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: 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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“…For example, in 4D if the complex zeroth order quadratic and cubic Weyl invariants I and J satisfy 27J 2 = I 3 , then the Weyl tensor is of type II (or more special; e.g., type D) [7,10] . The real and imaginary parts of this complex syzygy can be expressed using invariants of the Weyl tensor not containing duals.…”

Section: Type Ii/dmentioning

confidence: 99%

“…This is equivalent to the (12th order) real syzygies given in [14] from the associated six dimensional (bivector) system with 6 D 6 = 0 and 6 D 5 = 0. Applying the condition 4 D 4 = 0 to the 4D trace-free Ricci tensor we obtain the (12th order) syzygy for the trace-free Ricci tensor to be of type II/D [10,14].…”

Section: Type Ii/dmentioning

confidence: 99%

Discriminating the Weyl type in higher dimensions using scalar curvature invariants

Coley

Hervik

2011

Gen Relativ Gravit

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Higher dimensional Lorentzian spacetimes are of considerable interest in current theoretical physics. It is possible to algebraically classify any tensor in a Lorentzian spacetime of arbitrary dimensions using alignment theory. In the case of the Weyl tensor, and using bivector theory, the associated Weyl curvature operator will have a restricted eigenvector structure for algebraic types II and D, which leads to necessary conditions on the discriminants of the associated characteristic equation which can be manifestly expressed in terms of polynomial scalar curvature invariants. The use of such necessary conditions in terms of scalar curvature invariants will be of great utility in the study and classification of black hole solutions in more than four dimensions.

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“…Thus spacetimes not of these types provide with examples of spaces where such a Wick rotation is not allowed. Non-Wick-rotatable metrics include the classes of Kundt metrics [13] in Lorentzian geometry, and the Walker metrics [14] of more general signature. Also the metrics considered in [15] are in general non-Wick-rotatable metrics.…”

Section: Discussionmentioning

confidence: 99%