arXiv subjects

Nathalie Tassotti

Publications and source records attributed to Nathalie Tassotti.

3 recordsLinked to original sources

arXiv2026

Modeling of point charges with distributions, regularizations, and generalized functions

We apply regularization and generalized function techniques to the classical electromagnetic field of a point-charge, following a strategy by the physicist A. Gsponer 2007-2009, thereby extending it and adding rigor.. We show how the Liénard-Wiechert potential emerges essentially from the basic geometry of Minkowski space, namely by action of the d'Alembertian on a generating vector field, which is defined via a spacetime interval between an observer and the point-charge at retarded proper time. Furthermore, for a charged particle in its rest frame, we discuss generalized functions aspects of the electric monopole, magnetic dipole, electron singularity, and self-energy, where infinitely large generalized numbers occur whose concrete representations can be applied in field renormalization.

math-ph↗

arXiv2014

A positive mass theorem for low-regularity Riemannian metrics

We show that the positive mass theorem holds for continuous Riemannian metrics that lie in the Sobolev space $W^{2, n/2}_{loc}$ for manifolds of dimension less than or equal to $7$ or spin-manifolds of any dimension. More generally, we give a (negative) lower bound on the ADM mass of metrics for which the scalar curvature fails to be non-negative, where the negative part has compact support and sufficiently small $L^{n/2}$ norm. We show that a Riemannian metric in $W^{2, p}_{loc}$ for some $p > \frac{n}{2}$ with non-negative scalar curvature in the distributional sense can be approximated locally uniformly by smooth metrics with non-negative scalar curvature. For continuous metrics in $W^{2, n/2}_{loc}$, there exist smooth approximating metrics with non-negative scalar curvature that converge in $L^p_{loc}$ for all $p < \infty$.

math.DG↗

arXiv2012

A positive mass theorem for low-regularity metrics

We prove a positive mass theorem for continuous Riemannian metrics in the Sobolev space $W^{2, n/2}_{\mathrm{loc}}(M)$. We argue that this is the largest class of metrics with scalar curvature a positive a.c. measure for which the positive mass theorem may be proved by our methods.

math.DG↗