Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T06:16:31.355Z Has data issue: false hasContentIssue false
  • English
  • Français

The new potential for the Weyl tensor in N dimensions: gauge andwave equation

Published online by Cambridge University Press:  30 September 2008

A. Oscoz ,
E. Mediavilla ,
M. Serra-Ricart ,
S. Brian Edgar  and
J.M.M. Senovilla
S. Brian Edgar
Affiliation:
Matematiska Institutionen, Linköpings Universitet, 581 83, Linköping, Sweden
J.M.M. Senovilla
Affiliation:
Física Teórica, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain
Get access

Abstract

Although the Lanczos potential (a (2,1) form, Labc) for theWeyl tensor does not exist in dimensions greater than four, a newpotential (a (2,3) form, Pabcde, which coincides with thedouble dual of Labc in four dimensions) has recently beenshown to exist in all dimensions n ≥ 4.In this talk we investigate the question of gauge and discuss the structure of the new potential's wave equation whichis obtained from the Bianchi identities; identifying the gauge supplies us with a new direct proof of the existence of Pabcde via the Cauchy-Kowaleski theorem, as well as the foundation for more general investigations of the first order symmetric hyperbolic structure.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 30: Spanish Relativity Meeting - Encuentros Relativistas Españoles, ERE2007: Relativistic Astrophysics and Cosmology , 2008 , pp. 245 - 248
Copyright
© EAS, EDP Sciences, 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Edgar, S.B., 1994, Mod. Phys. Lett. A, 6, 479 CrossRef
Edgar, S.B., & Höglund, A., 2000, Gen. Rel. Grav., 32, 2307; 2002, Gen. Rel. Grav., 34, 2149 CrossRef
Edgar, S.B., & Höglund, A., 1997, Proc. Royal Society London, A., 453, 835
Edgar, S.B., & Senovilla, J.M.M., 2004, Class. Quantum Grav., 21, L133 CrossRef
Edgar, S.B., & Senovilla, J.M.M., 2006a, in A century of Relativity Physics, ERE 2006, XVIII Spanish Relativity Meeting, Oviedo, Spain, September 2005 Mornas, L., & Alonso, J.D., AIP, ed. (New York), 291
Edgar, S.B., & Senovilla, J.M.M., 2006b, J. Geom. Phys., 56, 2136
Lanczos, C., 1962, Rev. Mod. Phys., 34, 379 CrossRef
Senovilla, J.M.M., 2000, Class. Quan. Grav., 17, 2799 CrossRef
Senovilla, J.M.M., 2007, Gen. Rel. Grav., 39, 361 CrossRef