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This note aims at investigating two different situations where the classicalgeneral relativistic dynamics competes with the evolution driven by Hawkingevaporation. We focus, in particular, on binary systems of black holes emittinggravitational waves and gravitons, and on the cosmological evolution when blackholes are immersed in their own radiation bath. Several non-trivial featuresare underlined in both cases.

Einstein vs Hawking: Black hole binaries and cosmological expansion