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I have some questions concerning the calculations made by Hawking in the 80-90's using Euclidean (canonical) quantum gravity on gravitational instantons. Were those tunnelings only between identical closed FRW metrics (in the minisuperspace approximation where the only unfrozen mode is a(t) ) with different a (tunneling from $a_1$ to $a_2$) but with identical topology, or could those worm-holes represent topological changes or something more exotic?

I tried to read this paper: http://siba.unipv.it/fisica/articoli/P/Physical%20review%20D_vol.28_no.12_1983_pp.2060-2975.pdf (Hawking Hartle 1983) but couldn't clearly find the answer to my question. Said in other words, what kind of transitions can be described by these instantons processes? and, if Euclidean gravity is a dead-end as it seems widely considered today, are those results totally irrelevant nowadays?

Thank you.

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Isn't the Hartle-Hawking scenario a bit unusual when thought of as tunneling, because the "tunneling" is from a single point (presumably with "no" geometry) to the target three geometry (FRW slices), rather than from one three geometry to another? –  twistor59 Jul 11 '12 at 11:44
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