Cylindrically symmetric charged dust distributions in rigid rotation in general relativity

Som, M. M.; Raychaudhuri, A. K.

doi:10.1098/rspa.1968.0073

Cited by 104 publications

(21 citation statements)

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“…Remarkably, the answer is in the positive. These spacetimes were discovered by Som and Raychaudhuri in 1968 [11] as a class of solutions of Einstein-Maxwell equations with a charged dust source. These geometries have the same sort of causal pathologies as the Gödel metric, and like the latter, have sources which obey physically reasonable energy conditions.…”

Section: Raychaudhuri-som Geometriesmentioning

confidence: 99%

“…The analogy is further strengthened for stationary spacetimes, where not only is there an exact correspondence between different components of the metric and electric and magnetic fields (such that the geodesic equation can be exactly cast in the form of Lorentz force equation), but that given certain special stationary spacetimes, particles in them exhibit interesting phenemonena such as Landau levels and spatial non-commutativity. One such class of spacetimes was discovered by Som and Raychaudhuri and later re-derived using simple matter field configurations of electromagnetic and scalar fields by one of us (JG) and A. Das [11,12]. We will refer to them as SR spacetimes.…”

Section: Introductionmentioning

confidence: 99%

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Gravitational non-commutativity and Gödel-like spacetimes

Das

Gegenberg²

2008

Gen Relativ Gravit

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We derive general conditions under which geodesics of stationary spacetimes resemble trajectories of charged particles in an electromagnetic field. For large curvatures (analogous to strong magnetic fields), the quantum mechanicical states of these particles are confined to gravitational analogs of lowest Landau levels. Furthermore, there is an effective non-commutativity between their spatial coordinates. We point out that the Som-Raychaudhuri and Gödel spacetime and its generalisations are precisely of the above type and compute the effective non-commutativities that they induce. We show that the non-commutativity for Gödel spacetime is identical to that on the fuzzy sphere. Finally, we show how the star product naturally emerges in Som-Raychaudhuri spacetimes.

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Section: Raychaudhuri-som Geometriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gravitational non-commutativity and Gödel-like spacetimes

Das

Gegenberg²

2008

Gen Relativ Gravit

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“…Indeed, we have 27) which depend now on the three dimensionless parameters c 1 , c 2 and c 3 . Using the above variables the metric becomes c 2 4 ds 2 .…”

Section: Non-vanishing Cmentioning

confidence: 99%

“…As homogeneous space-times, they are of the Bianchi type IX (squashed S 3 , here as Gödel space), II (Heisenberg group) and VIII (elliptically squashed AdS 3 ). The second space is also known as Som-Raychaudhuri [27].…”

Section: Jhep04(2014)136mentioning

confidence: 99%

Holographic perfect fluidity, Cotton energy-momentum duality and transport properties

Mukhopadhyay

Petkou

Petropoulos

et al. 2014

J. High Energ. Phys.

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We investigate background metrics for 2 + 1-dimensional holographic theories where the equilibrium solution behaves as a perfect fluid, and admits thus a thermodynamic description. We introduce stationary perfect-Cotton geometries, where the Cotton-York tensor takes the form of the energy-momentum tensor of a perfect fluid, i.e. they are of Petrov type D t . Fluids in equilibrium in such boundary geometries have non-trivial vorticity. The corresponding bulk can be exactly reconstructed to obtain 3 + 1-dimensional stationary black-hole solutions with no naked singularities for appropriate values of the black-hole mass. It follows that an infinite number of transport coefficients vanish for holographic fluids. Our results imply an intimate relationship between black-hole uniqueness and holographic perfect equilibrium. They also point towards a Cotton/energy-momentum tensor duality constraining the fluid vorticity, as an intriguing boundary manifestation of the bulk mass/nut duality.

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“…Owing to its striking properties, the cosmological solution presented by Gödel has a well-recognized importance and has to a large extent motivated the investigations on rotating cosmological space-times within the framework of general relativity. Particularly, the search for rotating Gödel-type space-times has received a good deal of attention in recent years, and the literature on these geometries is fairly large today see [21] - [34] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Riemannian space-times of Gödel type in five dimensions

Rebouças

Teixeira

1998

Journal of Mathematical Physics

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The five-dimensional (5D) Riemannian Gödel-type manifolds are examined in light of the equivalence problem techniques, as formulated by Cartan. The necessary and sufficient conditions for local homogeneity of these 5D manifolds are derived. The local equivalence of these homogeneous Riemannian manifolds is studied. It is found that they are characterized by two essential parameters m 2 and ω : identical pairs (m 2 , ω) correspond to locally equivalent 5D manifolds. An irreducible set of isometrically nonequivalent 5D locally homogeneous Riemannian Gödel-type metrics are exhibited. A classification of these manifolds based on the essential parameters is presented, and the Killing vector fields as well as the corresponding Lie algebra of each class are determined. It is shown that apart from the (m 2 = 4 ω 2 , ω = 0) and (m 2 = 0, ω = 0) classes the homogeneous Riemannian Gödel-type manifolds admit a seven-parameter maximal group of isometry (G 7 ). The special class (m 2 = 4 ω 2 , ω = 0) and the degenerated Gödel-type class ( m 2 = 0, ω = 0) are shown to have a G 9 as maximal group of motion. The breakdown of causality in these classes of homogeneous Gödel-type manifolds are also examined.

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Cylindrically symmetric charged dust distributions in rigid rotation in general relativity

Cited by 104 publications

References 0 publications

Gravitational non-commutativity and Gödel-like spacetimes

Gravitational non-commutativity and Gödel-like spacetimes

Holographic perfect fluidity, Cotton energy-momentum duality and transport properties

Riemannian space-times of Gödel type in five dimensions

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