Localized energy of gravitational waves

Tuesday, Mar 5th 

Simone Speziale, Aix Marseille University
Localized energy of gravitational waves
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By Jorge Pullin (LSU)

The idea of associating a local energy density to a gravitational field has been problematic in general relativity. In electromagnetism, a region with an electric or magnetic field contains an energy whose density (energy per unit volume at a point) is proportional to the field squared. In gravity, however, things are more complicated. This is illustrated by a thought experiment first proposed by Einstein. Consider an observer in a windowless elevator and two situations: a) the elevator is in outer space, where gravity is negligible, but accelerating at a rate of 9.8 m/s2, the acceleration of gravity on Earth, and b) it is motionless on the surface of the Earth. In both cases if the observer releases a mass, it will fall to the floor with the same acceleration. No experiment carried out in the elevator can distinguish both situations. Therefore, one could not claim that one has an energy content and the other does not.

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.