Hidden symmetries, null geodesics, and photon capture in the Sen black hole

Hioki, Kenta; Miyamoto, Umpei

doi:10.1103/physrevd.78.044007

Cited by 155 publications

(140 citation statements)

References 45 publications

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“…The relationship between the existence of the PCKY tensor and the uniqueness of this spacetime was first addressed in [106], [107]. Other recent papers which deal with hidden symmetries or the subjects addressed in this thesis are, for example, [2], [3], [1], [4], [53], [94], [100], [105], [117], [194], [234], [235].…”

Section: When the Einstein Equations With The Cosmological Constant Amentioning

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: When the Einstein Equations With The Cosmological Constant Amentioning

confidence: 99%

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

2007

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“…The shadows (or apparent shapes) of nonrotating black holes are circular, but rotating ones present a deformation caused by the spin [12,13]. This topic has been recently considered by several authors [10,[14][15][16][17][18][19][20][21][22][23][24][25], both in Einstein gravity and in modified theories, since it is expected that direct observation of black holes will be possible in the near future [25][26][27]. In that case, the analysis of the shadows will be a useful tool for obtaining properties of astrophysical black holes and comparing different gravitational theories.…”

Section: Introductionmentioning

confidence: 99%

Shadow of a Kaluza-Klein rotating dilaton black hole

2013

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“…Rotating black holes present apparent shapes or shadows with an optical deformation due to the spin [19,20], instead of being circles as in the case of non-rotating ones. This topic has been reexamined by several authors in the last few years [17,[21][22][23][24][25][26][27][28], with the expectation that the direct observation of black holes will be possible in the near future [28]; therefore the study of the shadows will be useful for measuring the properties of astrophysical black holes. Optical properties of rotating braneworld black holes were studied by Schee and Stuchlik [29].…”

Section: Introductionmentioning

confidence: 99%

Shadow of a rotating braneworld black hole

2012

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We investigate the shadow cast by a rotating braneworld black hole, in the Randall-Sundrum scenario. In addition to the angular momentum, the tidal charge term deforms the shape of the shadow. For a given value of the rotation parameter, the presence of a negative tidal charge enlarges the shadow and reduces its deformation with respect to Kerr spacetime, while for a positive charge, the opposite effect is obtained. We also analyze the case in which the combination of the rotation parameter and the tidal charge results in a naked singularity. We discuss the observational prospects corresponding to the supermassive black hole at the Galactic center.

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Hidden symmetries, null geodesics, and photon capture in the Sen black hole

Cited by 155 publications

References 45 publications

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Shadow of a Kaluza-Klein rotating dilaton black hole

Shadow of a rotating braneworld black hole

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