The lightcone of Gödel-like spacetimes

G Dautcourt (1)

1 AEI - Max-Planck-Institut für Gravitationsphysik ( Albert-Einstein-Institut )

A study of the lightcone of the Gödel universe is extended to the socalled Gödel-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 Gödel metric. The quasi-periodic refocussing of cone generators with startling lens properties, discovered by Ozsváth and Schücking for the lightcone of a plane gravitational wave and also found in the Gödel universe, is a feature of the whole Gödel 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.

Mots clés: 02.40.Xx; 04.20.-q; 02.40.Hw; 04.20.Jb; 04.20.Gz

G Dautcourt. The lightcone of Gödel-like spacetimes. Classical and Quantum Gravity, 2010, 27 (22), pp.225024. ⟨10.1088/0264-9381/27/22/225024⟩. ⟨hal-00643030⟩