# What do the components of light velocity look like in polar coordinates?

The Schwarzschild solution makes use of polar coordinates, and I'm wondering how the different components of velocity of light change with the position. Might I get some examples of light velocity vectors (in units of $c$ such that $\langle 1,0,0,0\rangle$ is the velocity vector for a light ray moving radially away from the black hole at the speed of light)?

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