Please tell me the best place to publish a breakthrough papers on Gravitation. The best choice is surely journal Nature. Slightly less good place is Nature Physics. Less good place is Physical Review Letters, then Physical Review D, Annals of Physics, European Journal of Physics C. Please continue. But please exclude from the list journals of Fully Open Access - I have no money or funding.
Generally speaking if you have to ask:
"Where should I publish my breakthrough paper in X?" then probably (at least one of these):
1. You aren't really familiar with sub-field X;
2. Your paper isn't the breakthrough you think it is; and
3. even if it is, your manuscript isn't ready for publication because you haven't done a through literature search.
The last point is really important. Even if your result seems totally out of the blue, there is some connections to prior work. Finding relevant references would show you the relevant journals for such a submission and also shows the editors, referees, and readers that you understand the current state of the field you are writing about.
Now, once you've identified the candidates, picking the journal can be tricky: Do I go flashy (Nature, Science, PRL), or do I want a more specialized journal?
On your journal listings:
1. Nature,
2. Nature Physics,
Nature (and Science) almost never publish mathematical theory. (They do publish a little numerical experiment, a.k.a. simulation.) I've not looked at Nature Physics to see their content (not sure if we subscribe, and I wish they'd stick to their prime purpose: making star bio researchers feel special).
3. Physical Review Letters,
4. Physical Review D,
PRL and PRD definitely publish theory and gravitation. A revolutionary work in gravitation is likely to long to be published in PRL.
5. Annals of Physics,
6. European Journal of Physics C,
7. ?
The EJP doesn't have a part C, but the European Physical Journal C does publish gravitation.
I'm not surprised you missed "Classical and Quantum Gravity" and there are probably a couple more.
If this is about that manuscript you posted recently, it's not ready, so do yourself a favor and don't send it to a journal and annoy an editor after wasting their time.
Finally, while there are a few active and retired researchers on this site, there is really no expectation that you can get good advice about which physics journal to send a paper on gravitation to.
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