The Geodesics in Gödel's Universe

Chandrasekhar, S.; Wright, James P.

doi:10.1073/pnas.47.3.341

Cited by 76 publications

(47 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(38) it is easy to compute the geodesics and extend the analysis already performed for AdS and Gödel's metrics [12,4]. We find that for µ > 1, the qualitative behavior of the geodesics are the same as in Gödel's space.…”

supporting

confidence: 63%

Gödel metric as a squashed anti-de Sitter geometry

Rooman

Spindel

1998

Class. Quantum Grav.

110

129

View full text Add to dashboard Cite

We show that the non flat factor of the Gödel metric belongs to a one parameter family of 2+1 dimensional geometries that also includes the antide Sitter metric. The elements of this family allow a generalizationà la Kaluza-Klein of the usual 3+1 dimensional Gödel metric. Their lightcones can be viewed as deformations of the anti-de Sitter ones, involving tilting and squashing. This provides a simple geometric picture of the causal structure of these space-times, anti-de Sitter geometry appearing as the boundary between causally safe and causally pathological spaces. Furthermore, we construct a global algebraic isometric embedding of these metrics in 4+3 or 3+4 dimensional flat spaces, thereby illustrating in another way the occurrence of the closed timelike curves.

show abstract

supporting

confidence: 63%

Gödel metric as a squashed anti-de Sitter geometry

Rooman

Spindel

1998

Class. Quantum Grav.

110

129

View full text Add to dashboard Cite

show abstract

“…However, in Gödel universe there is no Cauchy horizon containing closed null geodesics. Also from the analysis of free motion in Gödel spacetime, we know that the geodesic motion do not follow a CTC [4,5].…”

Section: Final Remarks Conclusionmentioning

confidence: 99%

“…The study of geodesics showed that this spacetime is geodesically complete (and so singularity free) [4,5].…”

Section: Introductionmentioning

confidence: 98%

“…The source of this geometry is a perfect fluid with constant density ρ and no pressure (p = 0). Einstein's equation's with a cosmological constant Λ are satisfied if between Ω, Λ and ρ the following relation holdsThe study of geodesics showed that this spacetime is geodesically complete (and so singularity free) [4,5].Furthermore, because the universe is spacetime homogeneous, there are CTCs through every event [6] (hence the causal violation is not localized to some small region).In the last decade many authors have studied features of quantum field theory on a spacetime background that contains CTCs but most of the papers are dealing with confined causality violating spacetime.In these, CTCs are confined within some regions and there exist at least one region free of them; the regions with CTCs are separated from the well behaved spacetime by Cauchy horizons. Being a highly symmetric homogeneous spacetime, Gödel spacetime is an excellent model to investigate questions of principle related to the quantization of fields propagating on curved background, the interaction with a global vorticity and the issues related to the lack of global hyperbolicity.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Quantum Effects in a Rotating Spacetime

Radu

Astefanesei

2002

Int. J. Mod. Phys. D

View full text Add to dashboard Cite

The behavior of a arbitrary coupled quantum scalar field is studied in the background of the Gödel spacetime. Closed forms are derived for the effective action and the vacuum expectation value of quadratic field fluctuations by using ζ-function regularization. Based on these results, we argue that causality violation presented in this spacetime can not be removed by quantum effects. Introduction and motivationWhether or not the laws of physics permit the existence of closed timelike curves (CTCs) is one the important problems in the research field of modern theoretical physics. A number of familiar spacetimes make it clear that general relativity, as it is normally formulated, does not exclude the violation of causality in large scale, despite its local Lorentzian character. 1 where Ω and m are constants; m 2 can be continued to negative values, for m 2 → 0 obtaining SomRaychaudhuri spacetime [3]. The solution originally proposed by Gödel corresponds to the case m 2 = 2Ωwhere Ω ≥ 0 is a constant parameter related to the vorticity of the matter, and −∞ < t, z < ∞, 0 ≤ r < ∞, 0 < ϕ ≤ 2π. The source of this geometry is a perfect fluid with constant density ρ and no pressure (p = 0). Einstein's equation's with a cosmological constant Λ are satisfied if between Ω, Λ and ρ the following relation holdsThe study of geodesics showed that this spacetime is geodesically complete (and so singularity free) [4,5].Furthermore, because the universe is spacetime homogeneous, there are CTCs through every event [6] (hence the causal violation is not localized to some small region).In the last decade many authors have studied features of quantum field theory on a spacetime background that contains CTCs but most of the papers are dealing with confined causality violating spacetime.In these, CTCs are confined within some regions and there exist at least one region free of them; the regions with CTCs are separated from the well behaved spacetime by Cauchy horizons. Being a highly symmetric homogeneous spacetime, Gödel spacetime is an excellent model to investigate questions of principle related to the quantization of fields propagating on curved background, the interaction with a global vorticity and the issues related to the lack of global hyperbolicity. Even if one's primary interest is in quantum field theory in a confined causality violating spacetime, we hope that, by widening the context to Gödel spacetime, one may achieve a deeper appreciation of the theory. In particular, one may hopes to attain more general features of a quantum field propagating in a nonglobally hyperbolic spacetime, whether or not containing a Cauchy horizon. Of particular interest is the question whether causality violation which occurs in Gödel spacetime implies divergence of vacuum polarization fluctuations and may be removed by quantum effects. Thus it seems important to study the vacuum polarization for different physical fields in this background. 2A different reason to study quantum field theory (QFT) in this background emerges from the fact ...

show abstract

“…Chandrasekhar and Wright [5] computed the geodesies of the Godel universe G, and they found that this function r is bounded above by the value ro = ln(l + \/2) on the null geodesies which pass through (i, x, y, z) = (0,0,0,0). Projecting r down to a function f on M, we see that f is bounded by ln(l + y/2) on the G-pseudochains passing through (r,x,y) = (0,0,0).…”

Section: Lorentz Metrics and Pseudochainsmentioning

confidence: 99%

Chains on CR Manifolds and Lorentz Geometry

Koch¹

1988

Transactions of the American Mathematical Society

View full text Add to dashboard Cite

ABSTRACT. We show that two nearby points of a strictly pseudoconvex CR manifold are joined by a chain. The proof uses techniques of Lorentzian geometry via a correspondence of Fefferman. The arguments also apply to more general systems of chain-like curves on CR manifolds. Introduction.If M is a nondegenerate CR manifold, its Fefferman metric is a conformal class of pseudo-Riemannian metrics on a circle bundle over M. The various CR invariants of M may be described in terms of the conformal geometry of this metric; the description of chains in this setting is especially appealing. Recently, H. Jacobowitz showed that chains on a strictly pseudo-convex CR manifold connect pairs of nearby points. This paper presents a new proof of Jacobowitz's result which makes use of the Fefferman correspondence. We hope that this approach will yield new insights into the behavior of chains.We begin with a definition of an abstract CR manifold of hypersurface type. We then sketch briefly a construction due to Lee [15] of the pseudo-Riemannian Fefferman manifold associated to a CR manifold, and discuss the special properties of such manifolds. Much of this discussion applies to a slightly more general class of pseudo-Riemannian manifolds.We then proceed with our proof that chains on a strictly pseudoconvex CR manifold connect pairs of sufficiently nearby points. This proof applies also to the "pseudochains" associated to the more general pseudo-Riemannian manifolds discussed above. Finally, we discuss an example of a CR manifold with a system of pseudochains which are not chains. CR manifoldsand chains. An abstract almost CR manifold of hypersurface type is an odd-dimensional orientable manifold M2n+1 (which we shall always take to be smooth) together with a field of tangent hyperplanes 772™ on which a (smooth) complex structure J, J: H -> 77 linear, J2 = -id [h, is given. This J is called a CR structure tensor on M. An almost CR manifold is called a CR manifold if its Nijenhuis torsion tensor,vanishes for X, Y E 77; a CR structure satisfying this condition is said to be formally integrable.Let 9 E T*M be a one-form which annihilates 77. A choice of such a one-form is called a pseudo-Hermitian structure on M. The almost CR structure on M is said to be nondegenerate if 0 A (d0)n ^ 0; this condition is independent of the choice of 6._

show abstract

The Geodesics in Gödel's Universe

Abstract: PHYSICS: CHANDRASEKHAR AND WRIGHT 341 equation technique of dynamic programming. Some reductions which are useful from the computational viewpoint are indicated, and several applications to radar and communication system theory are sketched.

Cited by 76 publications

References 0 publications

Gödel metric as a squashed anti-de Sitter geometry

Gödel metric as a squashed anti-de Sitter geometry

Quantum Effects in a Rotating Spacetime

Chains on CR Manifolds and Lorentz Geometry

Contact Info

Product

Resources

About