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arXiv · 2104.03805

Light-like parallel vector fields and Einstein equations of gravity

Isidore Mahara·Célestin Kurujyibwami·Venuste Nyagahakwa
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Abstract

We prove that, contrary to the situation with time-like and space-like parallel vector fields, there are real gravitational fields satisfying Einsteins equations of gravity and admitting nontrivial light-like parallel vector fields; we solve completely the field equations under this geometric constraint and obtain through Bianchi identities an interesting property for the Riemann curvature tensor corresponding with a real gravitational field admitting a nontrivial parallel vector field. The solutions we obtained turn out to be generically wave-like and then we prove by a geometric method that this class of solutions is quite different from the class of solutions corresponding with spherical waves.

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Isidore Mahara, Célestin Kurujyibwami, Venuste Nyagahakwa. 2021-04-08. Light-like parallel vector fields and Einstein equations of gravity. https://arxiv.org/abs/2104.03805

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