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A focal point of a hypersurface along an orthogonal geodesic is a point where a nonzero normal Jacobi field arising from variations of the initial point vanishes. Beyond the first focal point, that geodesic no longer locally maximizes proper time from a spacelike initial hypersurface.

The vector $T^a$ is the tangent to a reference member of a one-parameter family of affinely parametrized geodesics. The Jacobi field $Y^a$ is the infinitesimal connecting vector from that geodesic to a neighboring one at equal parameter. The geodesic deviation equation states that curvature determines their relative acceleration.