Geodesic Deviation — Spacetime Curvature & Tidal Forces

D²ξᵘ/dτ² = −Rᵘᵥρσ uᵛ ξρ uσ. A sphere of test particles in curved spacetime distorts under tidal forces. Near a mass M: radial stretching, transverse squeezing — the "spaghettification" signature of GR tidal tensor.

Mass M (GM/c²r³ × r₀²) 0.50 N geodesics 20 Initial radius 0.12

D²ξ/dτ² = −R(u,ξ,u) | Radial: +2M/r³ξᵣ (stretch) | Transverse: −M/r³ξ⊥ (squeeze)