Hello, I need to find the angular velocity using Schwarzschild metric. At first I wrote the metric in general form and omitted the co-latitude: ds2=T*dt2+R*dr2+Φ*dφ2 and wrote a Lagrangian over t variable: L = √(T+R*(dr/dt)2+Φ*(dφ/dt)2) now I can use the Euler–Lagrange equations for φ variable and note that L does not depend on φ. dL/d(dφ/dt) = const => Φ*(dφ/dt) / L = const => dφ/dt = const * L / Φ The result is that dφ/dt depends on dr/dt because L contains dr/dt term. But there is one more way that I can calculate the dφ/dt. I can write the Lagrangian over new τ variable: L = √(T*(dt/dτ)2+R*(dr/dτ)2+Φ*(dφ/dτ)2) I can do the same calculations for dφ/dτ and dt/dτ variables: dL/d(dφ/dτ) = const => Φ*(dφ/dτ) / L = const => dφ/dτ = const * L / Φ dL/d(dt/dτ) = const => T*(dt/dτ) / L = const => dt/dτ = const * L / T Now I can divide one over another and get dφ/dt = const * T / Φ The result is that the angular velocity does not depend on dr/dt. Could someone help me what is wrong with one of my calculation?