### Citations

766 |
Mathematical Theory of Black Holes
- Chandrasekhar
- 1983
(Show Context)
Citation Context ...icity of the analysis we have chosen equal values of the rotation parameters. The case with unequal rotation parameters is currently under study [8]. The motion in the Kerr space-time is presented in =-=[9, 10]-=-. Some special cases of the motion in 5D Myers-Perry space-times are studied in [11], where it was shown that there are no stable circular orbits in the equatorial place, and in [12] scattering and ca... |

214 |
Black holes in higher dimensional space-times
- Myers, Perry
- 1986
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Citation Context ...onserved quantities of a test particle and characterize the motion by their zeros. We exemplify the efficiency of the analytical method on the orbits of test particles. 1 Introduction The Myers-Perry =-=[1]-=- space-time is a higher dimensional generalization of the Kerr space-time which describes rotating black holes in more than four dimensions. Interest in higher dimensional gravity is a result of the s... |

124 |
Theory of Functions of a Complex Variable,
- Markushevich
- 1965
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Citation Context ...3 − g2y − g3 := P3(y) , (25) where g2 = b22 12 − b1b3 4 , g3 = b1b2b3 48 − b0b 2 3 16 − b 3 2 216 . (26) The differential equation (25) is of elliptic type and is solved by the Weierstraß’ ℘–function =-=[30]-=- y(γ) = ℘ (γ − γ′in; g2, g3) , (27) where γ′in = γin + ∫∞ yin dy√ 4y3−g2y−g3 with yin = b3 4 uin + b2 12 . Then the solution of (5) acquires the form u = 1 b3 ( 4℘ (γ − γ′in; g2, g3)− b2 3 ) . (28) 4.... |

30 |
holes in theories with large extra dimensions: A review,” Int
- Kanti, “Black
- 1986
(Show Context)
Citation Context ...f the higher dimensional black hole solutions in vacuum and in supergravity theory is presented in [2, 3] and a discussion of the physical properties of higher dimensional black holes is addressed in =-=[4]-=-. General Kerr-de Sitter and Kerr-NUT-AdS metrics in all dimensions are presented in [5, 6]. A very good motivation to study the higher dimensional black holes is proposed in [7]. In the present work ... |

9 |
Analytic solutions of the geodesic equation in higher dimensions, Phys
- Hackmann, Kagramanova, et al.
- 2008
(Show Context)
Citation Context ...δr20 −K) b1 = 4a 4 ( E2 − δ)+ 4K(r20 − 2a2) + 8r20(a2E2 + aE(Φ + Ψ)) b0 = 4a 2 ( r20 (aE +Ψ+Ψ) 2 −Ka2 ) . (18) The list of the possible orbits reads (For an explanation of the names of the orbits see =-=[29]-=-): 1. Escape Orbits (EO) in the region [u1,∞) with u1 > u+. The EO does not cross the horizons. 2. Two-world escape orbits (TEO) in the region [u1,∞) with |u1| ≤ u− (a) Terminating escape orbits (TEOs... |

4 |
Analytic treatment of complete and incomplete geodesics in Taub–NUT space–times, Phys
- Kagramanova, Kunz, et al.
(Show Context)
Citation Context ... Θξ define the angles of two cones which confine the motion of the test particles. (A similar feature appears in Taub-NUT, Kerr-(de Sitter) and Reissner-Nordström (for charged particles) space–times =-=[27, 23, 28]-=-.) The discriminant D = b2ξ − 4aξcξ of the polynomial Θξ can be written as D = 16c1c2. The existence of real zeros of Θξ requires D ≥ 0. And with the conditions (13) this is fulfilled. The inequalitie... |

4 | Kagramanova,Geodesics of electrically and magnetically charged test particles in the Reissner– Nordström space–time: analytical solutions, in preparation
- Grunau, V
(Show Context)
Citation Context ... Θξ define the angles of two cones which confine the motion of the test particles. (A similar feature appears in Taub-NUT, Kerr-(de Sitter) and Reissner-Nordström (for charged particles) space–times =-=[27, 23, 28]-=-.) The discriminant D = b2ξ − 4aξcξ of the polynomial Θξ can be written as D = 16c1c2. The existence of real zeros of Θξ requires D ≥ 0. And with the conditions (13) this is fulfilled. The inequalitie... |

3 |
Black holes galore
- Emparan
- 2008
(Show Context)
Citation Context ...ssociated with a change of the fundamental value of the Planck mass in higher dimensions). A review of the higher dimensional black hole solutions in vacuum and in supergravity theory is presented in =-=[2, 3]-=- and a discussion of the physical properties of higher dimensional black holes is addressed in [4]. General Kerr-de Sitter and Kerr-NUT-AdS metrics in all dimensions are presented in [5, 6]. A very go... |

2 |
The Geometry of Kerr Black Holes (A.K
- O’Neil
- 1995
(Show Context)
Citation Context ...icity of the analysis we have chosen equal values of the rotation parameters. The case with unequal rotation parameters is currently under study [8]. The motion in the Kerr space-time is presented in =-=[9, 10]-=-. Some special cases of the motion in 5D Myers-Perry space-times are studied in [11], where it was shown that there are no stable circular orbits in the equatorial place, and in [12] scattering and ca... |

1 |
Analytic treatment of geodesics in general fivedimensional Myers-Perry space–times, under preparation
- Kagramanova, Kunz, et al.
(Show Context)
Citation Context ... particles in the 5D Myers-Perry space-times. For simplicity of the analysis we have chosen equal values of the rotation parameters. The case with unequal rotation parameters is currently under study =-=[8]-=-. The motion in the Kerr space-time is presented in [9, 10]. Some special cases of the motion in 5D Myers-Perry space-times are studied in [11], where it was shown that there are no stable circular or... |