Identity
Sep8-11, 03:44 AM
How do you prove that for the schwarzschild metric,
ds^2 = -\left(1-\frac{2M}{r}\right)dt^2+\left(1-\frac{2M}{r}\right)^{-1}dr^2+r^2d\theta^2+r^2\sin^2\theta d\phi^2,
g_{ij}p^ip^j=-m^2, where p^i is the momentum 4-vector?
Do you have to convert p from cartesian to polar coordinates first?
ds^2 = -\left(1-\frac{2M}{r}\right)dt^2+\left(1-\frac{2M}{r}\right)^{-1}dr^2+r^2d\theta^2+r^2\sin^2\theta d\phi^2,
g_{ij}p^ip^j=-m^2, where p^i is the momentum 4-vector?
Do you have to convert p from cartesian to polar coordinates first?