Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 52 min ago
Peer-reviewedCC BY-ND 4.0Annales de l'Institut Fourier

Conformal Scattering of Maxwell Potentials

  • Jean-Philippe Nicolas
  • Grigalius Taujanskas
Open at sourcePDFDOICite

Abstract

We construct a complete conformal scattering theory for finite energy Maxwell potentials on a class of curved, asymptotically flat spacetimes with prescribed smoothness of null infinity and a non-zero ADM mass. In order to define the full set of scattering data, we construct a Lorenz-like gauge which makes the field equations hyperbolic and non-singular up to null infinity, and reduces to an intrinsically solvable ODE on null infinity. We develop a method to solve the characteristic Cauchy problem from this scattering data based on a theorem of Hörmander. In the case of Minkowski space, we further investigate an alternative formulation of the scattering theory by using the Morawetz vector field instead of the usual timelike Killing vector field.

Related

  1. Electromagnetic Potentials via the Extended Maxwell System
    Rainer Picard, Sascha Trostorff, Marcus Waurick
    arXivPreprintarXiv licenceFull textAnalysis & PDEsMathematical physicsarXiv
  2. Sharp Time Decay and Scattering of Small Data Solutions to the Relativistic Vlasov-Maxwell System
    Grace Mattingly, Stephen Pankavich, Jonathan Ben-Artzi
    arXivPreprintarXiv licenceFull textAnalysis & PDEsMathematical physicsarXiv
  3. Freezing Calderón: Robust Preconditioning for Maxwell Scattering under Shape Uncertainty
    Paul Escapil-Inchauspé, Carlos Jerez-Hanckes
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv
  4. Modified scattering for the 3D Hartree equation with singular external potentials
    Mengyi Xie
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Monopole-Fermion Scattering from Twisted Conformal Boundary States
    Clay Córdova, Diego García-Sepúlveda, Lian-Tao Wang +1
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCondensed matterarXiv

Cite

BibTeXRIS
BibTeX
@article{nicolas2026conformal,
  title = {{Conformal Scattering of Maxwell Potentials}},
  author = {Jean-Philippe Nicolas and Grigalius Taujanskas},
  journal = {Annales de l'Institut Fourier},
  year = {2026},
  month = jul,
  doi = {10.5802/aif.3733},
  url = {https://hal.science/hal-05780744v1},
  note = {CC BY-ND 4.0},
}
RIS
TY  - JOUR
TI  - Conformal Scattering of Maxwell Potentials
AU  - Jean-Philippe Nicolas
AU  - Grigalius Taujanskas
PY  - 2026
DA  - 2026/07/10
JO  - Annales de l'Institut Fourier
DO  - 10.5802/aif.3733
UR  - https://hal.science/hal-05780744v1
AB  - We construct a complete conformal scattering theory for finite energy Maxwell potentials on a class of curved, asymptotically flat spacetimes with prescribed smoothness of null infinity and a non-zero ADM mass. In order to define the full set of scattering data, we construct a Lorenz-like gauge which makes the field equations hyperbolic and non-singular up to null infinity, and reduces to an intrinsically solvable ODE on null infinity. We develop a method to solve the characteristic Cauchy problem from this scattering data based on a theorem of Hörmander. In the case of Minkowski space, we further investigate an alternative formulation of the scattering theory by using the Morawetz vector field instead of the usual timelike Killing vector field.
SN  - 0373-0956
SN  - 1777-5310
ER  -