Electromagnetic quasinormal modes of D-dimensional black holes

López-Ortega, A.

doi:10.1007/s10714-006-0358-2

Cited by 47 publications

(57 citation statements)

References 79 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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“…Generic master equations governing the highly-damped quasi-normal frequencies [QNFs] of one-horizon, two-horizon, and even three-horizon spacetimes can be obtained through either semi-analytic [1,2,3] or monodromy techniques [4,5,6,7,8,9,10,11,12,13,14,15,16]. (For general background, see also [17,18,19,20,21,22,23,24,25,26,27].)…”

Section: Introductionmentioning

confidence: 99%

Generic master equations for quasi-normal frequencies

Skákala

Visser

2010

J. High Energ. Phys.

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Generic master equations governing the highly-damped quasi-normal frequencies [QNFs] of one-horizon, two-horizon, and even three-horizon spacetimes can be obtained through either semi-analytic or monodromy techniques. While many technical details differ, both between the semi-analytic and monodromy approaches, and quite often among various authors seeking to apply the monodromy technique, there is nevertheless widespread agreement regarding the general form of the QNF master equations. Within this class of generic master equations we can establish some rather general results, relating the existence of "families" of QNFs of the form ω a,n = (offset) a + in (gap) to the question of whether or not certain ratios of parameters are rational or irrational.

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“…[17] we showed that the modes I and II of the electromagnetic field have a different spectrum of the de Sitter QN frequencies (for fixed angular momentum number l, the QN frequencies have different parity in odd dimensions, while in even dimensions a finite number of QN frequencies, which depend on the spacetime dimension, are different). 7 For the massless Dirac field propagating in the BTZ black hole we can simplify the equations of motion to Schrödinger type equations with effective potentials equal to (see expression (74) in [17] and Ref. [35])…”

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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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Electromagnetic quasinormal modes of D-dimensional black holes

Cited by 47 publications

References 79 publications

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Generic master equations for quasi-normal frequencies

Dirac quasinormal modes of D-dimensional de Sitter spacetime

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