On parallel null 1planes in spacetime
Abstract
A parallel null 1plane in spacetime consists of a recurrent field of null vectors. It is shown that spacetime may admit at most two such fields, unless it is flat. Canonical forms for the corresponding metrics and Petrov types for the Weyl tensor are determined. Considering the recurrence vector of the plane as an appropriate candidate for the electromagnetic potential, the LienardWiechert formula is generalized to curved spacetime. This approach relates the retarded distance with the Riemannian curvature of spacetime.
 Publication:

Nuovo Cimento B Serie
 Pub Date:
 July 1976
 DOI:
 10.1007/BF02723348
 Bibcode:
 1976NCimB..34..169O
 Keywords:

 Einstein Equations;
 Gravitation Theory;
 Relativity;
 SpaceTime Functions;
 Astronomical Models;
 Astrophysics;
 Canonical Forms;
 Energy Distribution;
 Maxwell Equation;
 Minkowski Space;
 Partial Differential Equations;
 Riemann Manifold;
 Tensors;
 Universe;
 Astrophysics