Quasi-local holography and quasi-local mass of classical fields in Minkowski spacetime

Details Quasi-local holography and quasi-local mass of classical fields in Minkowski spacetime Quasi-local holography and quasi-local mass of classical fields in Minkowski spacetime

2004-11-30

arxiv.org/abs/gr-qc/0411148v2

Class.Quant.Grav. 22 (2005) 855-878

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages; reference added, typos corrected, discussion is improved; appearing in Class. Q. Grav

Scientific paper

10.1088/0264-9381/22/5/007

The 2-surface characterization of special classical radiative Higgs-, Yang-Mills and linear zero-rest-mass (l.z.r.m) fields with any spin is investigated. We determine all the zero quasi-local mass Higgs- and Yang-Mills field configurations with compact semisimple gauge groups, and show that they are plane waves (provided the Higgs field is massless and linear) and appropriate generalizations of plane waves (`Yang-Mills pp-waves'), respectively. A tensor field (generalizing the energy-momentum tensor for the Maxwell field and of the Bel-Robinson tensor for the linearized gravitational field) is found by means of which the pp-wave nature of the solutions of the l.z.r.m. field equations with any spin can be characterized equivalently. It is shown that these radiative Yang-Mills and l.z.r.m. fields, given on a finite globally hyperbolic domain D, are determined completely by certain unconstrained data set on a closed spacelike 2-surface, the `edge of D'. These pure radiative solutions are shown to determine a dense subset in the set of solutions of various (Yang-Mills and l.z.r.m.) field equations. Thus for these field configurations some `classical quasi-local holography' holds.

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