Conjugate points along null geodesics in a class of spacetimes

Abstract

The existence and location of conjugate points along null geodesics in Taub's vacuum spacetime is investigated in detail. It is shown that every null geodesic ? not confined in a t-z plane contains two pairs of segments (M, ) and (N, ) such that each point p in M (resp. N) has a unique conjugate point along ? that is located in (resp. ) and vice versa, and what is more interesting, if p and are conjugate points along ? with J+(p), then I+(p). This presents a realistic example illustrating that there do exist null geodesics emanating from p that can get into I+(p) before meeting a point conjugate to p. All results are generalized to a class of spacetimes.