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PeterDonis

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I am trying to derive the radial momentum equation in the equatorial Kerr geometry obtained from the equation

$$

(P+\rho)u^\nu u^r_{;\nu}+(g^{r\nu}+u^ru^\nu)P_{,r}=0 \qquad

$$

Where are you getting this equation from? It doesn't look anything like a "radial momentum equation" in Kerr geometry, since Kerr geometry is a vacuum geometry so ##\rho = P = 0## everywhere.

since the equation only involves radial derivatives

The equation has a covariant derivative, which includes terms in the connection coefficients that involve other values of ##\nu## besides ##r##.

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