A construction of 4D spacetimes from 3D contact manifolds with degenerate metrics yields Einstein solutions with null dust and cosmic strings, including two arbitrary density functions.
Okumura, Tohoku Mathematical Journal14, 135 (1962), publisher: Tohoku University, Mathematical Institute
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Spacetime constructed from a contact manifold with a degenerate metric
A construction of 4D spacetimes from 3D contact manifolds with degenerate metrics yields Einstein solutions with null dust and cosmic strings, including two arbitrary density functions.