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Up to the first conjugate point, a geodesic between two points is unique. Beyond this, there can be multiple geodesics connecting two points.
Suppose we have a [[Lorentzian manifold]] with a [[geodesic congruence]]. Then, at a conjugate point, the [[expansion parameter]] θ in [[Raychaudhuri's equation]] becomes negative infinite in a finite amount of proper time, indicating that the geodesics are focusing to a point. This is because the cross-sectional area of the congruence becomes zero, and hence the rate of change of this area (which is what θ represents) diverges negatively.
==Examples==
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