Proper Accelerations of Time-Like Curves near a Null Geodesic
TIAN Gui-Hua1,2, ZHAO Zheng2
1School of Science, Beijing University of Posts and Telecommunications, Beijing 100876
2Department of Physics, Beijing Normal University, Beijing 100875
Proper Accelerations of Time-Like Curves near a Null Geodesic
TIAN Gui-Hua1,2;ZHAO Zheng2
1School of Science, Beijing University of Posts and Telecommunications, Beijing 100876
2Department of Physics, Beijing Normal University, Beijing 100875
Abstract： It is well known that when given a null geodesic γ0(λ) with a point r in (p,q) conjugate to p along γ0(λ), there will be a variation of γ0(λ) which can give a time-like curve from p to q. Here we prove that the time-like curves coming from the above-mentioned variation (with the second derivative β2 ≠ 0) have a proper acceleration A = √AaAa which approaches infinity as the time-like curve approaches the null geodesic. Because the curve obtained from variation of the null geodesic must be everywhere time-like, we also discuss the constraint of the‘acceleration’βa0 of the variation vector field on the null geodesic γ0(λ). The acceleration βa0 of the variation vector field Za on the null geodesic γ0(λ) cannot be zero.
2003, Vol. 20 
