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Acta Physica Sinica (Overseas Edition), 1996, Vol. 5(3): 161-169    DOI: 10.1088/1004-423X/5/3/001
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CONJUGATE POINTS ALONG NULL GEODESICS IN A CLASS OF SPACETIMES

KUANG ZHI-QUAN (邝志全)a, LIANG CAN-BIN (梁灿彬)b, WU YUE-JIANG (吴月江)b
a Institute of Mathematics, Academia Sinica, Beijing 100080, China; b Department of Physics, Beijing Normal University, Beijing 100875, China
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 $\eta$ not confined in a t-z plane contains two pairs of segments ($\mathcal{M}$, $\widetilde{\mathcal{M}}$) and ($\mathcal{N}$ $\widetilde{\mathcal{N}}$) such that each point p in $\mathcal{M}$(resp.$\mathcal{N}$) has a unique conjugate point $\widetilde{p}$ along $\eta$ that is located in $\widetilde{\mathcal{M}}$ (resp. $\widetilde{\mathcal{N}}$) and vice versa, and what is more interesting, if p and $\widetilde{\mathcal{p}}$ are conjugate points along $\eta$ with $\widetilde{\mathcal{p}}$∈J+(p), then $\widetilde{\mathcal{p}}$∈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.
Received:  27 April 1995      Accepted manuscript online: 
PACS:  04.20.-q (Classical general relativity)  
  02.40.-k (Geometry, differential geometry, and topology)  
Fund: Project supported by the National Natural Science Foundation of China.

Cite this article: 

KUANG ZHI-QUAN (邝志全), LIANG CAN-BIN (梁灿彬), WU YUE-JIANG (吴月江) CONJUGATE POINTS ALONG NULL GEODESICS IN A CLASS OF SPACETIMES 1996 Acta Physica Sinica (Overseas Edition) 5 161

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