Assume we have a system of say two bodies which are orbiting each other. Now assume that we wish to find an equation of the orbits of the two gravitational sources. Do they follow a ‘geodesical’ path, if we assume that the sources may or may not be singularities, which in this case may require a puncture method or so I’ve heard.
I have also read several articles which suggest that it does move ‘geodesically’ if one does not take into account the self-interaction of the space-time field. If we were to take into account the self-interaction, back-reaction and what nots, will it still move ‘geodesically’ in the metric of the entire manifold?
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