Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Asymptotics to all orders of the Euler-Darboux equation in a triangle
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2019 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 471, no 1-2, p. 180-196Article in journal (Refereed) Published
Abstract [en]

In Einstein's theory of relativity, the interaction of two collinearly polarized plane gravitational waves can be described by a Goursat problem for the Euler Darboux equation in a triangular domain. In this paper, using a representation of the solution in terms of Abel integrals, we give a full asymptotic expansion of the solution near the diagonal of the triangle. The expansion is related to the formation of a curvature singularity of the spacetime. In particular, our framework allows for boundary data with derivatives which are singular at the corners. This level of generality is crucial for the application to gravitational waves.

Place, publisher, year, edition, pages
Academic Press INC Elsevier Science , 2019. Vol. 471, no 1-2, p. 180-196
Keywords [en]
Euler-Darboux equation, Gravitational waves, Einstein's theory of relativity, Collinear polarization
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-240688DOI: 10.1016/j.jmaa.2018.10.071ISI: 000452581100011OAI: oai:DiVA.org:kth-240688DiVA, id: diva2:1277092
Note

QC 20190109

Available from: 2019-01-09 Created: 2019-01-09 Last updated: 2019-01-09Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Search in DiVA

By author/editor
Mauersberger, Julian
By organisation
Mathematics (Dept.)
In the same journal
Journal of Mathematical Analysis and Applications
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 56 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf