Conjugate points along null geodesics in a class of spacetimes

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 η not confined in a t-z plane contains two pairs of segments ( M , ) and ( N , Ñ) such that each point p in M (resp. N ) has a unique conjugate point along η that is located in (resp. Ñ) and vice versa, and what is more interesting, if p and are conjugate points along η 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.