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    On product spacetime with 2-sphere of constant curvature
    (2000-10-10) Dadhich, Naresh
    If we consider the spacetime manifold as product of a constant curvature 2-sphere (hypersphere) and a 2-space, then solution of the Einstein equation requires that the latter must also be of constant curvature. There exist only two solutions for classical matter dis- tribution which are given by the Nariai (anti) metric describing an Einstein space and the Bertotti - Robinson (anti) metric describing a uniform electric field. These two solutions are transformable into each other by letting the timelike convergence density change sign. The hy- perspherical solution is anti of the spherical one and the vice -versa. For non classical matter, we however find a new solution, which is electrograv dual to the flat space, and describes a cloud of string dust of uniform energy density. We also discuss some interesting features of the particle motion in the Bertotti - Robinson metric.