**Simone Speziale, Aix Marseille University**

Localized energy of gravitational waves

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Over the years this has led to confusion and to attempts to create local energy densities that are problematic, namely, they are ambiguous and coordinate-dependent. For many years the issue of if gravitational waves carried an energy flux was contentious, eventually being settled in the1960's. The end result is that one cannot define a local energy density but must discuss energy considerations only considering complete regions of space-time and studying them from far away. Mathematically this requires treating fields at infinity. One can define energies and fluxes in an invariant way at infinity only.

This talk discussed some of the subtleties involved and presents a framework where infinity and other regions of interest, like the horizons that surround black holes, can be treated in a unified way. This may lead to insights into what are the true physical degrees of freedom that one should consider quantizing in a theory of quantum gravity.