1. The problem statement, all variables and given/known data I was researching relativity, and stumbled across this: "General relativity introduces a third force that attracts the particle slightly more strongly than Newtonian gravity, especially at small radii. This third force causes the particle's elliptical orbit to precess..." Is this accurate? If so, how does it work?
it introduces a correction term to the Newtonian calculation which I guess you could view as a "third force" and this is responsible for the precession of the perihelion of Mercury etc.
Now I'm kind of curious what the first two 'forces' are. Doing gravitation in GR doesn't even usually involve talking about 'forces' except in a perturbative sense. It's all geodesics, isn't it?
Yes, that is exactly what perplexes me. In the context of general relativity, gravity is not a force, in the same way that there is no centrifugal force: it is a consequence of the coordinate system. Of course, this quote was from Wikipedia, but I've been following it for quite some time and have not seen it amended.
It's probably what latentcorpse said. You can cast the GR solution as a 'correcting' force to the force of gravity. But even in Newtonian theory, there's only one 'force', that's gravity. Centrifugal 'force' is not a force, it's an acceleration. I think you understand the issue. Probably best not to be overly concerned with what Wikipedia says.
I am not sure where the quote is coming from, but the effective potential of an object orbiting a point source in GR does have three terms. Differentiate and you get a total force with three contributions: 1. Inverse square (Newtonian gravity) 2. Inverse cube (Centrifugal force) 3. Inverse fourth power (GR "correction") The thread has implied it, but I think this is where the talk of a "third" force is coming from. The first two produce the standard elliptical orbit and the third is a kind of perturbation causing precession. This is a poor-man's way to calculate the precession of Mercury, etc.