The boundary of Gödel's spacetime and the chronology protection conjecture

Details The boundary of Gödel's spacetime and the chronology protection conjecture The boundary of Gödel's spacetime and the chronology protection conjecture

2012-01-05

arxiv.org/abs/1201.1129v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Comments added in figures.Some corrections in the text. Added comments on the spectral distance

Scientific paper

We present a homogenous anisotropic conformal spacetime manifold that provide an example of Hawking's chronology protection conjecture in three-dimensional gravity theory. The solution is based upon the fact that the seven-dimensional group of the automorphism of the Heisenberg motion group H1{\times}U(1), modulo discrete sub-group \Gamma, is the symmetry group of the sub-Riemannian (SR)- manifold, boundary of the Cauchy-Riemann (CR)-manifold, allowing the existence of positive mass, momentum, angular-momentum and timelike-translation. It is shown that many mirror symmetric self-similar G\"odel's surfaces are hidden behind a Cauchy spacelike surface so that causality violation is not visible from outside.

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