[NT/RBRC seminar] Conserved non-Noether charge in general relativity:Physical definition vs. Noether's 2nd theorem

by Prof. Sinya Aoki (Yukawa institute, Kyoto University)

Friday 1 Apr 2022, 09:00 → 11:00 US/Eastern

https://bnl.zoomgov.com/j/1601261155?pwd=dUpkOHBWb21sRll4SnRCUC83MjRKQT09

In this talk, I make a close comparison of  a covariant definition of an energy/entropy in general relativity, recently proposed by our collaboration,  with existing definitions of energies  such as the one from the pseudo-tensor and the quasi-local energy.
I show that existing definitions of energies in general relativity are conserved charges from the Noether's 2nd theorem
for the general coordinate transformation, whose conservations are merely identities implied by the local symmetry and always hold without using equations of motion.  Thus  none of existing definitions in general relativity reflects the dynamical properties of the system, need for a physical definition of an energy.
In contrast, our new definition of the energy/entropy in general relativity is generically a conserved non-Noether  charge and  gives physically sensible results for various cases such as the black hole mass, the gravitational collapse, and the expanding universe, while existing definitions sometimes lead to
unphysical ones including zero and infinity.
I conclude that our proposal is more physical than existing definitions of energies. Our proposal makes it possible to define almost uniquely the covariant and  conserved energy/entropy in general relativity, which brings some implications to future investigations.