2 research outputs found
The Internal Spin Angular Momentum of an Asymptotically Flat Spacetime
In this paper we investigate the manner in which the internal spin angular
momentum of a spinor field is encoded in the gravitational field at asymptotic
infinity. The inclusion of internal spin requires us to re-analyze our notion
of asymptotic flatness. In particular, the Poincar\'{e} symmetry at asymptotic
infinity must replaced by a spin-enlarged Poincar\'{e} symmetry. Likewise, the
generators of the asymptotic symmetry group must be supplemented to account for
the internal spin. In the Hamiltonian framework of first order Einstein-Cartan
gravity, the extra generator comes from the boundary term of the Gauss
constraint in the asymptotically flat context. With the additional term, we
establish the relations among the Noether charges of a Dirac field, the Komar
integral, and the asymptotic ADM-like geometric integral. We show that by
imposing mild restraints on the generating functionals of gauge transformations
at asymptotic infinity, the phase space is rendered explicitly finite. We
construct the energy-momentum and the new total (spin+orbital) angular momentum
boundary integrals that satisfy the appropriate algebra to be the generators of
the spin-enlarged Poincar\'{e} symmetry. This demonstrates that the internal
spin is encoded in the tetrad at asymptotic infinity. In addition, we find that
a new conserved and (spin-enlarged) Poincar\'{e} invariant charge emerges that
is associated with the global structure of a gauge transformation.Comment: V2: No major changes, journal reference adde