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The Jacobi equation D²J/dt²+R(J,T)T=0 governs how nearby geodesics diverge. For constant curvature K:
• K>0 (sphere): J∝sin(√K·t) — geodesics converge, meet at antipodal points.
• K=0 (flat): J∝t — linear divergence.
• K<0 (hyperbolic): J∝sinh(√|K|·t) — exponential divergence = chaos.
This is the geometric heart of tidal forces in GR.