BOUNDLESS EXPANSE 3D

🌐 Gravitational Lensing & Einstein Ring

Einstein radius · Paczynski amplification · microlensing light curve · dark matter
Key formula: θ_E = √(4GM/c² · D_LS/(D_L·D_S)) A(u) = (u²+2)/(u·√(u²+4)) [Paczynski]

Massive objects deflect light (Einstein 1915, confirmed 1919). Einstein radius θ_E = √(4GM/c² · D_LS/(D_L·D_S)). At perfect alignment: Einstein ring. Microlensing amplification A(u) = (u²+2)/(u√(u²+4)) — a symmetric light curve peak. Bullet Cluster 2006: gravitational lensing maps proved dark matter exists separately from hot gas. Gravitational lensing measures H₀ independent of the CMB, helping resolve the Hubble tension.

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