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 \eta not confined in a t-z plane contains two pairs of segments (\mathcalM, \widetilde\mathcalM) and (\mathcalN \widetilde\mathcalN) such that each point p in \mathcalM(resp.\mathcalN) has a unique conjugate point \widetildep along \eta that is located in \widetilde\mathcalM (resp. \widetilde\mathcalN) and vice versa, and what is more interesting, if p and \widetilde\mathcalp are conjugate points along \eta with \widetilde\mathcalp∈J⁺(p), then \widetilde\mathcalp∈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.