MG11 
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On the zeros of spinor fields and an orthonormal frame gauge

We had proposed (in connection with a positive energy proof/localization) certain rotational gauge conditions for a preferred orthonormal frame on a Riemannian manifold. For certain physically interesting cases (dimensions 2, 3 & 4) such frames can be constructed from spinors (regarded as rotation-dilations) which solve the Dirac or Witten equations---with the important exception of points at which the spinor field vanishes. Are such zero points a serious problem? Here, using explicit examples, we show that spinor zeros really can happen. But we also argue that solutions with zeros are quite exceptional; for generic metrics and boundary data there are no zeros. We conclude that the "special orthonormal frame" gauge conditions can be used essentially without reservations.

Quasilocal energy for cosmological models

Our covariant Hamiltonian formalism gives a certain preferred Hamiltonian boundary term for quasilocal quantities which depends on the boundary conditions, plus a reference and displacement vector choice. With appropriate choices we found the quasilocal energy for the cosmological models. Homogeneous choices give vanishing energy for all regions of Bianchi class A models and positive energy for class B. Isotropic choices give energies proportional to the curvature parameter k: ie, vanishing for the flat case, positive for the closed model and negative(!) for the open model. Our values are consistent with the requirement that the energy vanishes for closed models. We have some conclusions regarding the best reference choice and two quasilocal desiderata: positivity and zero energy iff Minkowski space.