ρ - TU Dortmund

physik.uni.dortmund.de

ρ - TU Dortmund

Octavian Micu TU Dortmund 2008/01/28

Curvature and Einstein’s Equations

Christofell symbol:

Geodesic Equation:

Γ λ µν = 1 2 gλσ (∂ µ g νσ + ∂ ν g σµ − ∂ σ g µν )

d 2 x µ

dλ 2

− dx ρ dx σ

Γµ ρσ

dλ dλ = 0

The Riemann tensor:

R ρ σµν = ∂ µ Γ ρ νσ − ∂ ν Γ ρ µσ + Γ ρ µλ Γλ νσ − Γ ρ νλ Γλ µσ

Ricci Tensor and Ricci Scalar (the Curvature Scalar):

R µν = R λ µλν, R = R µ µ = g µν R µν

Einstein’s field equations:

G µν = R µν − 1 2 Rg µν = −8πGT µν

5

More magazines by this user
Similar magazines