Recent content by Intrastellar

I haven't look at that yet. I meant in the original papers in the OP.

I looked at the first paper, but didn't quite spot the Aha! moment where the equation was derived. As I understood it, the derivation was left outside the paper for being too complex. Is my understanding correct ? Just that point particles were modeled as singularities

I understand that the derivation in the paper is entirely classical, my question is in regards to the use of singularities generally to substitute for point particles following geodesics. Is that something that we expect to carry through to a theory of quantum gravity ?

Since I am reading the papers and trying to make sense of them, I will meanwhile ask a question: Do we expect that particles are related in any way to singularities in quantum gravity ?

Thank you very much! I will check out the papers.

You don't need to know, you derive the trajectories from the EFE, and compare them with those of the geodesic equation.

Yes, except that I want to reach this conclusion without assuming the geodesic equation, starting just from the EFES.

How can you say that there is no analytic solutions when you allow approximation as part of the definition of analytical solution ? There is, in the approximation that one of them has zero mass! Anyway, my question is more that is there a general argument that one can make for why such a result...

Perhaps I am using the word analytically incorrectly. What I meant is symbolically or mathematically, through algebra and calculus, and by taking approximations where necessary.

Do you need an analytical solution to check such a property of trajectories? Surely the question is simpler than to require the full GR simulation of two black holes.

Great, thanks! Now my remaining question is: is it possible to reflect this fact analytically ?

Perhaps a better question is : if you solve EFEs numerically for far away black holes, will the black holes approximately satisfy the geodesic equation in their approach ?

What I have in mind is you take the equations obeyed by two far away black holes and approximate them to get some notion of trajectory and coordinates of these two objects, and then derive that they will approach each other following a particular trajectory using EFEs, then that would...

Nononono I mean derived from the EFE as an approximation.

What about as an approximation ? I assume that to derive something that looks like the geodesic equation you have to take a number of approximations.