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Pervect has https://www.physicsforums.com/showpost.php?p=1046874&postcount=17" for radial and tangential gravitational accelerations of a moving particle in Schwarzschild coordinates.

[tex]

\frac{d^2 r}{d t^2} = \frac {3 m{{\it v_r}}^{2}}{ \left( r-2\,m \right) r} + \left( r-2\,m \right) \left( {{\it v_\phi}}^{2}-{\frac {m}{{r}^{3}}} \right)

[/tex]

[tex]

\frac{d^2\phi}{d t^2} = -\frac {2 {\it v_r}\,{\it v_\phi}\, \left( r -3\,m \right) }{ \left( r-2\,m \right) r}

[/tex]

where [itex]v_r =dr/dt[/itex], [itex]v_\phi = d\phi/dt[/itex], [itex]m[/itex] the mass of the primary and [itex]r,\phi[/itex] the Schwarzschild coordinate parameters.

Does anyone know of an equivalent set of equations for the Kerr metric, at least for movement along the equator of a rotating black hole?

[tex]

\frac{d^2 r}{d t^2} = \frac {3 m{{\it v_r}}^{2}}{ \left( r-2\,m \right) r} + \left( r-2\,m \right) \left( {{\it v_\phi}}^{2}-{\frac {m}{{r}^{3}}} \right)

[/tex]

[tex]

\frac{d^2\phi}{d t^2} = -\frac {2 {\it v_r}\,{\it v_\phi}\, \left( r -3\,m \right) }{ \left( r-2\,m \right) r}

[/tex]

where [itex]v_r =dr/dt[/itex], [itex]v_\phi = d\phi/dt[/itex], [itex]m[/itex] the mass of the primary and [itex]r,\phi[/itex] the Schwarzschild coordinate parameters.

Does anyone know of an equivalent set of equations for the Kerr metric, at least for movement along the equator of a rotating black hole?

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