# Can fictitious forces always be described by gravity fields in General Relativity?

I was debating a geocentrist online who said that Einstein and a bunch of other physicists admitted a geocentric framework is valid. I replied that this was technically correct, but if you wanted to adopt a framework where the Earth is stationary and non-rotating, you would need to introduce gravity fields throughout the entire universe which pushed everything else around.

Right after saying this, I worried that I might be spreading a misconception. I think it makes sense in light of Einstein's equivalence principle. I know this applies to uniform acceleration, but any acceleration could be considered as a bunch of tiny uniform accelerations stitched together, right? Maybe I'm missing something. Would what I described above be a valid way of thinking about a geocentric reference frame in General Relativity?

Edit: just to further clarify what I'm asking, I essentially want to know if all fictitious forces in any non-inertial reference frame can be described completely by introducing new gravity fields in GR. I changed the title of the question to reflect this.

• AFAIK it's an unsolved problem in GR whether the rotation is truly absolute or whether spinning the whole universe the other way around would get you the same measurements.
– g s
Commented Aug 22, 2023 at 2:41
• Or what "spinning the whole universe the other way around" even means ;) Commented Aug 22, 2023 at 8:11
• It is in fact true that a geocentric framework is allowed; this is simply mathematics. All the gymnastics with tensor fields etc are precisely because we want the laws of physics not to depend on your coordinate system, whether it is flat Euclidean or somehow curved. Even in Newtonian physics you can place Earth at the centre, but you just make it a lot harder to understand the motions of the planets. Commented Aug 22, 2023 at 9:13
• @j4nd3r53n I am not convinced people who haven't tried it appreciate just how hard "non-inertial" analysis is, even in Newtonian systems, e.g. en.wikipedia.org/wiki/Coriolis_force. Nice nick BTW ;) Commented Aug 22, 2023 at 10:33
• @m4r35n357 Well, in principle, it's simple enough; just tensors and Christoffel symbols ;-) The problem is doing it in practise. Commented Aug 22, 2023 at 12:47