On the stationary gravitational fields

Kloster, S.; Som, M. M.; Das, A.

doi:10.1063/1.1666759

Cited by 30 publications

(12 citation statements)

References 20 publications

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“…Now we are in a position to state and prove the main theorems of this section involving anisotropic fluids. (5). Moreover, let the stress-energy tensor T i j be that of an anisotropic fluid given by (42).…”

Section: Real Eigenvalues Of T I J and Anisotropic Fluid Modelsmentioning

confidence: 99%

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General solutions of Einstein’s spherically symmetric gravitational equations with junction conditions

Das

DeBenedictis

Tariq

2003

Journal of Mathematical Physics

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Einstein's spherically symmetric interior gravitational equations are investigated. Following Synge's procedure, the most general solution of the equations is furnished in case T 1 1 and T 4 4 are prescribed. The existence of a total mass function, M (r, t), is rigorously proved. Under suitable restrictions on the total mass function, the Schwarzschild mass M (r, t) = m, implicitly defines the boundary of the spherical body as r = B(t). Both Synge's junction conditions as well as the continuity of the second fundamental form are examined and solved in a general manner. The weak energy conditions for an arbitrary boost are also considered. The most general solution of the spherically symmetric anisotropic fluid model satisfying both junction conditions is furnished. In the final section, various exotic solutions are explored using the developed scheme including gravitational instantons, interior T -domains and D-dimensional generalizations. *

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Section: Real Eigenvalues Of T I J and Anisotropic Fluid Modelsmentioning

confidence: 99%

“…Signature changing metrics as well as the Euclidean gravitational instantons [5] are furnished. Next, T -domain [6] equations and general solutions are provided.…”

Section: Introductionmentioning

confidence: 99%

General solutions of Einstein’s spherically symmetric gravitational equations with junction conditions

Das

DeBenedictis

Tariq

2003

Journal of Mathematical Physics

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“…It is especially interesting and tempting to apply this method for the explicit calculation of new inhomogeneous QK metrics. Indeed, whereas a lot of the HK metrics of this sort was explicitly constructed (both in 4-and higher-dimensional cases, see, e.g., [30]- [33], [14]), not too many analogous QK metrics are known to date.…”

Section: Introductionmentioning

confidence: 99%

U(1)×U(1) quaternionic metrics from harmonic superspace

2002

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We construct, using harmonic superspace and the quaternionic quotient approach, a quaternionic-Kähler extension of the most general two centres hyper-Kähler metric. It possesses U (1) × U (1) isometry, contains as special cases the quaternionic-Kähler extensions of the Taub-NUT and Eguchi-Hanson metrics and exhibits an extra oneparameter freedom which disappears in the hyper-Kähler limit. Some emphasis is put on the relation between this class of quaternionic-Kähler metrics and self-dual Weyl solutions of the coupled Einstein-Maxwell equations. The relation between our explicit results and the recent general ansatz of Calderbank and Pedersen for quaternionic-Kähler metrics with U (1) × U (1) isometries is traced in detail.

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“…It is well known that the antisymmetric part ω a [bc] is related to the structure functions defined by the Lie bracket [e a , e b ] = c c ab e c by ω a 36) and the self-dual form J 1 = e 1 ∧ e 2 + e 3 ∧ e 4 . Then by use of (2.21) one obtain that…”

Section: Relation With the Plebanski-finley Conformal Structuresmentioning

confidence: 99%

Heterotic geometry without isometries

Исаев¹,

Santillán²

2005

J. High Energy Phys.

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We present some properties of hyperkahler torsion (or heterotic) geometry in four dimensions that make it even more tractable than its hyperkahler counterpart. We show that in d = 4 hypercomplex structures and weak torsion hyperkahler geometries are the same. We present two equivalent formalisms describing such spaces, they are stated in the propositions of section 1. The first is reduced to solve a non-linear system for a doublet of potential functions, first found by Plebanski and Finley. The second is equivalent to finding the solutions of a quadratic Ashtekar-Jacobson-Smolin like system, but without a volume preserving condition. This is why heterotic spaces are simpler than usual hyperkahler ones. We also analyze the strong version of this geometry. Certain examples are presented, some of them are metrics of the Callan-Harvey-Strominger type and others are not. In the conclusion we discuss the benefits and disadvantages of both formulations in detail. * Bogoliubov Laboratory of Theoretical Physics, JINR, 141 980 Dubna, Moscow Reg., Russia; isae-vap@thsun1.jinr.ru, firenzecita@hotmail.com and osvaldo@thsun1.jinr.ru J 3 = −e 1 ⊗ e 4 + e 4 ⊗ e 1 − e 2 ⊗ e 3 + e 3 ⊗ e 2 , and the action of (2.20) over the tangent space T M x is defined by J 1 (e 1 ) = e 2 , J 1 (e 2 ) = −e 1 , J 1 (e 3 ) = e 4 , J 1 (e 4 ) = −e 3 , J 2 (e 1 ) = e 3 , J 2 (e 2 ) = −e 4 , J 2 (e 3 ) = −e 1 , J 2 (e 4 ) = e 2 , J 3 (e 1 ) = e 4 , J 3 (e 2 ) = e 3 , J 3 (e 3 ) = −e 2 , J 3 (e 4 ) = −e 1 .(2.19)The hyperkahler triplet (2.13) is given by J 1 = e 2 ∧ e 1 + e 4 ∧ e 3 J 2 = e 3 ∧ e 1 + e 2 ∧ e 4 (2.20)

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On the stationary gravitational fields

Cited by 30 publications

References 20 publications

General solutions of Einstein’s spherically symmetric gravitational equations with junction conditions

General solutions of Einstein’s spherically symmetric gravitational equations with junction conditions

U(1)×U(1) quaternionic metrics from harmonic superspace

Heterotic geometry without isometries

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