In general relativity, these equations are replaced by the Einstein field equations in the trace-reversed form R μ μ ν ν = K ( T μ μ ν ν − − 1 2 T g μ μ ν ν ) for some constant, K, and the geodesic equation d 2 x α α d τ τ 2 = − − Γ Γ β β γ γ α α d x β β d τ τ d x γ γ d τ τ .