Total angular momentum from Dirac eigenspinors

Abstract

The eigenvalue problem for Dirac operators, constructed from two connections on the spinor bundle over closed spacelike 2-surfaces, is investigated. A class of divergence free vector fields, built from the eigenspinors, are found, which, for the lowest eigenvalue, reproduce the rotation Killing vectors of metric spheres, and provide rotation BMS vector fields at future null infinity. This makes it possible to introduce a well defined, gauge invariant spatial angular momentum at null infinity, which reduces to the standard expression in stationary spacetimes. The general formula for the angular momentum flux carried away be the gravitational radiation is also derived.

34 pages, typos corrected, four references added, appearing in Class. Quantum Grav

References in corpus (13)

• Dynamical Horizons and their Properties
• The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models
• Approximate Killing Vectors on S^2
• A generalized Damour-Navier-Stokes equation applied to trapping horizons
• Horizon energy and angular momentum from a Hamiltonian perspective
• Two dimensional Sen connections in general relativity
• Intrinsic angular momentum in general relativity
• The inequality between mass and angular momentum for axially symmetric black holes
• Angular momentum of isolated systems
• Two dimensional Sen connections and quasi-local energy-momentum
• On a class of 2-surface observables in general relativity
• On certain quasi-local spin-angular momentum expressions for large spheres near the null infinity
• The kernel of the edth operators on higher-genus spacelike two-surfaces

Cited by in corpus (7)

• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Intrinsic angular momentum for radiating spacetimes which agrees with the Komar integral in the axisymmetric case
• New spinorial approach to mass inequalities for black holes in general relativity
• On computations of angular momentum and its flux in numerical relativity
• Towards the quasi-localization of canonical GR
• A lower bound for the eigenvalues of the Sen-Witten operator on closed spacelike hypersurfaces
• New spinorial mass-quasilocal angular momentum inequality for initial data with marginally future trapped surface