Okay, so the only non-zero components of ##g_{\mu \nu}## are ## g_{tt} = 1- \frac{R_s}{r}## and ##g_{\phi \phi} = -r^2## which gives $$g(K_1,U) = g_{tt}\frac{dt}{d\tau} = (1-\frac{R_s}{r})\dot{t}$$ and $$g(K_4,U) = g_{\phi \phi}\frac{d\phi}{d\tau} = (-r^2)\dot{\phi}$$ which...
Okay thank you. Yes that was another trail I tried to follow. From what I have learned both ## \partial _t ## and ##\partial _\phi## are killing fields due to the spherical symmetri in Schwarzschild spacetime? So the derivative with respect to proper time ##\tau## of a scalarproduct between one...
Oh sorry of course, thank you I couldn´ t figure out how to use it!
So the line element is given by $$ ds^2 = (1- \frac{R_s}{r})dt^2 - (1- \frac{R_s}{r})^-1dr^2 - r^2d\Omega ^2$$
The object is orbiting at constant radius ##r## in the plane ## \theta = \frac{\pi}{2}##. I am supposed to find...
So the line element is given by $$ ds^2 = (1- \frac{R_s}{r})dt^2 - (1- \frac{R_s}{r})^{-1}dr^2 - r^2d\Omega ^2$$
The object is orbiting at constant radius ##r## in the plane ## \theta = \frac{\pi}{2}##. I am supposed to find the values of ##a## and ##b## in the 4-velocity given by: $$U =...