I would like to have a Star orbiting a Schwarzschild Black Hole if the the velocity and position vectors in the galaxy are given. The only thing that comes to mind is the Newtonian method.(adsbygoogle = window.adsbygoogle || []).push({});

The velocity and position vectors of the Star are:

[tex]v = {v_x, v_y, v_z)[/tex]

[tex]r = {x, y, z)[/tex]

where (no acceleration)

[tex]x = v_x * t +x_0[/tex]

[tex]y = v_y * t +y_0[/tex]

[tex]z = v_z * t +z_0[/tex]

convert to spherical

What is the method for GR?

Note:The Schwarzschild metric produces a non zero Riemann Tensor and a Ricci Flat as you well know.

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# Velocity and Position Vectors

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