Can point masses following geodesics and orbiting one another emit gravitational radiation?

I am a bit confused about this situation: according to general relativity, when two masses orbit one another, they emit graviational waves, which carry away certain energy. For example, check out this lecture notes. However, each mass (assuming it is a point mass) follows a geodesic, and so it is not accelerating in their local frame. So each mass individually should not produce radiation, at least when seen from their local frames. So what is going on here? Do they emit gravitational radiation or not? I would like to understand this from a more matehmatical point of view (what equations to use), and also conceptually (what exaclty is going on wrong with the reasoning).

I know that a similar question was asked here but I do not really understand the answer given there and that thread seems to be dead.

Interestingly, I found that Rovelli has a similar question in his new introductory book to GR but he does not answer it.

• related physics.stackexchange.com/questions/480249/… . I agree with the answers statement "A core aspect of the problem is that point particles do not make sense in general relativity (or similarly non-linear theories)." one needs quantization of gravity to avoid singularities May 9 at 13:55
• But what if we use small particles then? You could reformulate my question using small (not point) particles. What would be the answer in that case? May 9 at 14:09
• compllicated . see this hal.archives-ouvertes.fr/hal-01571766/document May 9 at 14:18
• > "according to general relativity, when two masses orbit one another, they emit graviational waves" -- I believe this is only according to linearized general relativity, which is not General Relativity. I think nobody has ever convincingly analyzed two body problem in full GR and shown emission of gravity waves, and loss of energy. It is mathematically amazingly difficult. May 9 at 23:49
• @JánLalinský You find numerical relativity simulations unconvincing? May 10 at 11:48

• You are welcome. Your question was indeed interesting. The equation I have meant is of course the famous $G_{\mu\nu}=\kappa~T{\mu\nu}$ applied to a (toy) spacetime generated by two masses. Such a case can be solved only numerically and fully transient (not static). Transient spacetime means transient geodesics. In a typical planetary system that effect is negligible but in case of orbiting black holes or neutron stars will be quite pronounced. I am not really expert on this field but it is what I think is a correct answer to your question. May 11 at 14:36