Spherically symmetric solutions in five-dimensional general relativity

Chodos, Alan; Detweiler, Steven

doi:10.1007/bf00756803

Cited by 236 publications

(236 citation statements)

References 8 publications

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“…The conditions of vanishing of constants (31) and (32) Because (in this case) the coefficients β and α 2,3 , and in consequence. w 2,3 could be arbitrary functions (see formulas (31), (32) and (33) and Eq.…”

Section: Taub-nut Metrics With Anisotropic Running Of Constants On S = ςmentioning

confidence: 96%

“…where the coefficients are some necessary smoothly class functions of type: 2,3 (r, θ ) , 4,5 (r, θ, s) (8) and (9) one introduce the anholonomic frames (anisotropic bases) 2,3 and N 5 2,3 = n 2,3 (they define an associated to some anholonomic frames (16) and (17), nonlinear connection, N -connection, structure, see details in Refs. [3,[15][16][17]20]).…”

Section: Metric Ansatzmentioning

confidence: 99%

“…(29) can be solved as independent linear algebraic equations for w 2,3 , wˆiβ + αˆi = 0,î = 2, 3. For zero matter sources this is a trivial result because in this case the conditions β = 0 and αˆi = 0 (see the formulas (31), (32) and (33)) are automatically fulfilled.…”

Section: General Properties Of Anisotropic Vacuum Solutionsmentioning

confidence: 99%

“…Much attention has been paid to off-diagonal metrics in higher-dimensional gravity beginning the Salam, Strathee and Perracci work [1] which showed that including offdiagonal components in higher-dimensional metrics is equivalent to including U (1), SU (2) E-mail addresses: vacaru@fisica.ist.utl.pt, sergiu_vacaru@yahoo.com (S.I. Vacaru), ovidiu@venus.nipne.ro (O. Tintareanu-Mircea). and SU (3) gauge fields.…”

Section: Introductionmentioning

confidence: 99%

“…The approach was developed by construction of various locally isotropic solutions of vacuum 5D Einstein equations describing 4D wormholes and/or flux tube gravitational-electromagnetic configurations (see Ref. [2]). …”

Section: Introductionmentioning

confidence: 99%

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Anholonomic frames, generalized Killing equations, and anisotropic Taub-NUT spinning spaces

2002

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By using anholonomic frames in (pseudo)-Riemannian spaces we define anisotropic extensions of Euclidean Taub-NUT spaces. With respect to coordinate frames such spaces are described by offdiagonal metrics which could be diagonalized by corresponding anholonomic transforms. We define the conditions when the 5D vacuum Einstein equations have as solutions anisotropic Taub-NUT spaces. The generalized Killing equations for the configuration space of anisotropically spinning particles (anisotropic spinning space) are analyzed. Simple solutions of the homogeneous part of these equations are expressed in terms of some anisotropically modified Killing-Yano tensors. The general results are applied to the case of the four-dimensional locally anisotropic Taub-NUT manifold with Euclidean signature. We emphasize that all constructions are for (pseudo)-Riemannian spaces defined by vacuum solutions, with generic anisotropy, of 5D Einstein equations, the solutions being generated by applying the moving frame method. 

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Section: Taub-nut Metrics With Anisotropic Running Of Constants On S = ςmentioning

confidence: 96%

Section: Metric Ansatzmentioning

confidence: 99%

Section: General Properties Of Anisotropic Vacuum Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Anholonomic frames, generalized Killing equations, and anisotropic Taub-NUT spinning spaces

2002

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Charged Rotating Black Hole from Five Dimensional Point of View

1987

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Abstract. It is shown that the usual characteristics of a black hole and of the physical fields produced by it obtain a unified geometrical meaning in the five-dimensional framework. Especidly, it is demonstrated that a solution for a rotating black hole with electric and scalar charges can he generated by a boost transformation of the fifth coordinate from the Kerr solution. (feladene, rotierende schwarze Lticher aus fiinf-dimensionalor SiehtInhaltsubersicht. Es wird gezeigt, wie die iiblichen Charakteristiken schw.wzer Ljcher iind der von ihnen erzeugten physikslischen Felder eine einheitliche geometrische Bedeutung im fiinfdimensionalen Formalismus erhalten. Speziell wird vorgefuhrt, daB man eine Losung fur ein rot,ierendea schwarzea Loch mit elektrischer und skalarer Ladung durch eine ,,b~ost"-Transformatsion der funften Koordinate aus der Ken-Losung erzeugen kann.Recently, the generalization of the standard EINSTEIN theory of gravitation to more than four dimensions by KALUZA [I] and KLEIN [ 2 ] is activly considered as a possible candidate for a unified field theory. The most important applications of this theories are early stages of the evolution of the Universe as well as compact astrophysical objects llke black holes. These cases are characterised by extremly strong fields and, therefore, specific properties of the more-dimensional theory may become significant. There is an extended literature on early cosmology in the framework of KALUZA-KLEIN theory ( 8 . e.g. [3-91). Concerning compact objects, in most of the papers (s. e.g. [ 10-151 the case of nonrotating black holes is considered.I n the present paper stationary axially symmet,ric five-dimensiod spaces are analysed, which correspond to regular four-dimensional rotating charged black holes.Suppose Mb to he a five-dimensional space-time covered by the metric GLin (-4, B = 0, 1, 2, 3; 5, sgii GAB = -+ + + +) providing a Killing vector field E.4(['),A EA = 2 f A~B E A 6 B = O ,(by ":" we denote the covariant derivative with respect to the 5-metric Gain). For 5 2 = fAtA we have the following relations:

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Charged Black Holes and Multidimensional Gravity

Бронников

1991

Annalen der Physik

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Spherically symmetric solutions in five-dimensional general relativity

Cited by 236 publications

References 8 publications

Anholonomic frames, generalized Killing equations, and anisotropic Taub-NUT spinning spaces

Anholonomic frames, generalized Killing equations, and anisotropic Taub-NUT spinning spaces

Charged Rotating Black Hole from Five Dimensional Point of View

Charged Black Holes and Multidimensional Gravity

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