Quasinormal modes of D-dimensional de Sitter spacetime

López-Ortega, A.

doi:10.1007/s10714-006-0335-9

Cited by 87 publications

(164 citation statements)

References 104 publications

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“…Another important direction of research is to study the quasinormal modes in higher dimensions. The results obtained in these directions so far restricts mainly to non-rotating (or not generally rotating) black holes (see, e.g., [112], [20], [21], [22], [23], [142], [143], [23], [24], [237], [127], [165], [164], [166], [144], [167], [138], [140], [34], [184], and references therein).…”

Section: Discussionmentioning

confidence: 99%

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

2007

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In this thesis we study higher-dimensional rotating black holes. Such black holes are widely discussed in string theory and brane-world models at present.We demonstrate that even the most general known Kerr-NUT-(A)dS spacetime, describing the general rotating higher-dimensional asymptotically (anti) de Sitter black hole with NUT parameters, is in many aspects similar to its fourdimensional counterpart. Namely, we show that it admits a fundamental hidden symmetry associated with the principal conformal Killing-Yano tensor. Such a tensor generates towers of hidden and explicit symmetries. The tower of Killing tensors is responsible for the existence of irreducible, quadratic in momenta, conserved integrals of geodesic motion. These integrals, together with the integrals corresponding to the tower of explicit symmetries, make geodesic equations in the Kerr-NUT-(A)dS spacetime completely integrable. We further demonstrate that in this spacetime the Hamilton-Jacobi, Klein-Gordon, and stationary string equations allow complete separation of variables and the problem of finding parallel-propagated frames reduces to the set of the first order ordinary differential equations. Moreover, we show that the Kerr-NUT-(A)dS spacetime is the most general Einstein space which possesses all these properties. We also explicitly derive the most general (off-shell) canonical metric admitting the principal conformal Killing-Yano tensor and demonstrate that such a metric is necessarily of the special algebraic type D of the higher-dimensional algebraic classification. The results presented in this thesis describe the new and complete picture of the relationship of hidden symmetries and rotating black holes in higher dimensions. PrefaceWhen in 1963 Kerr discovered an astrophysically relevant but relatively complicated metric describing the gravitational field of a rotating black hole, it seemed that no analytical predictions were possible even for the simplest particle geodesic motion. However, a 'miracle' happened, and it turned out that not only the geodesic motion can be analytically solved, but also the equations describing various perturbations of this background can be 'drastically' simplified. This opened a way for studying astrophysical processes, such as the plasma accretion around black holes, the radiation produced by infalling matter, the origin of jets, the production and propagation of waves produced in the vicinity of black holes, and it even led to estimates of the gravitational wave production in star collisions and galaxy merges. It also facilitated the study of more theoretical problems, such as the problem of stability of the Kerr solution, the calculation of the quasinormal modes, or the study of the Hawking radiation. A hidden symmetry responsible for this miracle can be mathematically described by a simple antisymmetric object, called the Killing-Yano tensor.Recently, higher-dimensional rotating black hole spacetimes have become of high interest due to various developments in gravity and high energy physic...

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Section: Discussionmentioning

confidence: 99%

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

2007

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“…Owing to its simplicity the propagation of classical fields in this spacetime has been studied, see for example [15]- [18], [21]- [27] and references therein. Its QNMs are defined as the solutions to the equations of motion for the classical fields that satisfy the boundary conditions [17], [22], [23]: (i) the field is regular at r = 0; (ii) the field is purely outgoing near the cosmological horizon.…”

Section: Introductionmentioning

confidence: 99%

Dirac quasinormal modes of D-dimensional de Sitter spacetime

López-Ortega

2007

Gen Relativ Gravit

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We find exact solutions to the Dirac equation in D-dimensional de Sitter spacetime. Using these solutions we analytically calculate the de Sitter quasinormal (QN) frequencies of the Dirac field. For the massive Dirac field this computation is similar to that previously published for massive fields of half-integer spin moving in four dimensions. However to calculate the QN frequencies of the massless Dirac field we must use distinct methods in odd and even dimensions, therefore the computation is different from that already known for other massless fields of integer spin.

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“…An interesting peculiarity of de-Sitter spacetime as compared to a black hole spacetime is that the quasi-normal frequencies are purely imaginary so that they describe the exponential decay only while generically there could be also oscillations 4 . In D spacetime dimensions there are two sets of the quasi-normal modes [21] …”

Section: Relation To the Quasi-normal Modesmentioning

confidence: 99%

The geometry of large causal diamonds and the no-hair property of asymptotically de Sitter space–times

Gibbons

Solodukhin²

2007

Physics Letters B

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In a previous paper we obtained formulae for the volume of a causal diamond or Alexandrov open set I + (p) ∩ I − (q) whose duration τ (p, q) is short compared with the curvature scale. In the present paper we obtain asymptotic formulae valid when the point q recedes to the future boundary I + of an asymptotically de-Sitter spacetime. The volume (at fixed τ ) remains finite in this limit and is given by the universal formula V (τ ) = 4 3 π(2 ln cosh τ 2 −tanh 2 τ 2 ) plus corrections (given by a series in e −tq ) which begin at order e −4tq . The coefficents of the corrections depend on the geometry of I + . This behaviour is shown to be consistent with the no-hair property of cosmological event horizons and with calculations of de-Sitter quasinormal modes in the literature.

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Quasinormal modes of D-dimensional de Sitter spacetime

Cited by 87 publications

References 104 publications

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Dirac quasinormal modes of D-dimensional de Sitter spacetime

The geometry of large causal diamonds and the no-hair property of asymptotically de Sitter space–times

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