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Journal Article

The lightcone of Gödel-like spacetimes

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Dautcourt,  G.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1009.5231
(Preprint), 266KB

CQG_27_22_225024.pdf
(Any fulltext), 389KB

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Citation

Dautcourt, G. (2010). The lightcone of Gödel-like spacetimes. Classical and quantum gravity, 27(22): 225024. doi:10.1088/0264-9381/27/22/225024.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-C96A-2
Abstract
A study of the lightcone of the Gödel universe is extended to the so-called G\"odel-like spacetimes. This family of highly symmetric 4-D Lorentzian spaces is defined by metrics of the form $ds^2=-(dt+H(x)dy)^2+D^2(x)dy^2+dx^2+dz^2$, together with the requirement of spacetime homogeneity, and includes the G\"odel metric. The quasi-periodic refocussing of cone generators with startling lens properties, discovered by Ozsv\'{a}th and Sch\"ucking for the lightcone of a plane gravitational wave and also found in the G\"odel universe, is a feature of the whole G\"odel family. We discuss geometrical properties of caustics and show that (a) the focal surfaces are two-dimensional null surfaces generated by non-geodesic null curves and (b) intrinsic differential invariants of the cone attain finite values at caustic subsets.