106 research outputs found
The classical point-electron in Colombeau's theory of nonlinear generalized functions
The electric and magnetic fields of a pole-dipole singularity attributed to a
point-electron-singularity in the Maxwell field are expressed in a Colombeau
algebra of generalized functions. This enables one to calculate dynamical
quantities quadratic in the fields which are otherwise mathematically
ill-defined: The self-energy (i.e., `mass'), the self-angular momentum (i.e.,
`spin'), the self-momentum (i.e., `hidden momentum'), and the self-force. While
the total self-force and self-momentum are zero, therefore insuring that the
electron-singularity is stable, the mass and the spin are diverging integrals
of delta-squared-functions. Yet, after renormalization according to standard
prescriptions, the expressions for mass and spin are consistent with quantum
theory, including the requirement of a gyromagnetic ratio greater than one. The
most striking result, however, is that the electric and magnetic fields differ
from the classical monopolar and dipolar fields by delta-function terms which
are usually considered as insignificant, while in a Colombeau algebra these
terms are precisely the sources of the mechanical mass and spin of the
electron-singularity.Comment: 30 pages. Final published version with a few minor correction
Expanding impulsive gravitational waves
We explicitly demonstrate that the known solutions for expanding impulsive
spherical gravitational waves that have been obtained by a "cut and paste"
method may be considered to be impulsive limits of the Robinson-Trautman vacuum
type N solutions. We extend these results to all the generically distinct
subclasses of these solutions in Minkowski, de Sitter and anti-de Sitter
backgrounds. For these we express the solutions in terms of a continuous
metric. Finally, we also extend the class of spherical shock gravitational
waves to include a non-zero cosmological constant.Comment: 11 pages, LaTeX, To appear in Class. Quantum Gra
On the completeness of impulsive gravitational wave space-times
We consider a class of impulsive gravitational wave space-times, which
generalize impulsive pp-waves. They are of the form ,
where is a Riemannian manifold of arbitrary dimension and carries
the line element with the line
element of and the Dirac measure. We prove a completeness result
for such space-times with complete Riemannian part .Comment: 13 pages, minor changes suggested by the referee
On the Geroch-Traschen class of metrics
We compare two approaches to semi-Riemannian metrics of low regularity. The maximally 'reasonable' distributional setting of Geroch and Traschen is shown to be consistently contained in the more general setting of nonlinear distributional geometry in the sense of Colombea
Regularity properties of distributions through sequences of functions
We give necessary and sufficient criteria for a distribution to be smooth or
uniformly H\"{o}lder continuous in terms of approximation sequences by smooth
functions; in particular, in terms of those arising as regularizations
.Comment: 10 page
Generalized Symmetries of Impulsive Gravitational Waves
We generalize previous \cite{AiBa2} work on the classification of
() symmetries of plane-fronted waves with an impulsive profile. Due
to the specific form of the profile it is possible to extend the group of
normal-form-preserving diffeomorphisms to include non-smooth transformations.
This extension entails a richer structure of the symmetry algebra generated by
the (non-smooth) Killing vectors.Comment: 18 pages, latex2e, no figure
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