Cosmological application of L0 geodesic and Levi-Civita connection. Raychaudhuri's 1955 equation for the expansion scalar θ = ∇_μ u^μ of a timelike geodesic congruence u^μ reads dθ/dτ = −(1/3)θ² − σ² + ω² − R_{μν}u^μu^ν, with shear σ²,…
Cosmological application of L0 geodesic and Levi-Civita connection. Raychaudhuri's 1955 equation for the expansion scalar θ = ∇_μ u^μ of a timelike geodesic congruence u^μ reads dθ/dτ = −(1/3)θ² − σ² + ω² − R_{μν}u^μu^ν, with shear σ²,…