Geodesic Deviation — Tidal Forces & Spacetime Curvature

The geodesic deviation equation: D²ξ^μ/dτ² = −R^μ_νρσ u^ν ξ^ρ u^σ relates separation ξ between nearby geodesics to the Riemann curvature tensor. Tidal forces in a Schwarzschild field squeeze radially and stretch tangentially — visualized as a ring of test particles near a mass.

Schwarzschild r_s = 2GM/c²:  |  Tidal acc aᵣ = −2GM/r³·δr (radial)  |  aₜ = +GM/r³·δθ (tangential squeezing)