Light rays in static spacetimes with critical asymptotic behavior: A variational approach
Let $mathcal{M}=mathcal{M}_{0}imes mathbb{R}$ be a Lorentzian manifold equipped with the static metric $langle cdot ,cdot angle _{z}=langle cdot ,cdot angle -eta (x)dt^{2}$. The aim of this paper is investigating the existence of lightlike geodesics joining a point $z_{0}=(x_{0},t_{0})$ to a line $g...
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| Format: | Article |
| Language: | English |
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Texas State University
2006-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2006/114/abstr.html |
| _version_ | 1818353959567360000 |
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| author | Valeria Luisi |
| author_facet | Valeria Luisi |
| author_sort | Valeria Luisi |
| collection | DOAJ |
| description | Let $mathcal{M}=mathcal{M}_{0}imes mathbb{R}$ be a Lorentzian manifold equipped with the static metric $langle cdot ,cdot angle _{z}=langle cdot ,cdot angle -eta (x)dt^{2}$. The aim of this paper is investigating the existence of lightlike geodesics joining a point $z_{0}=(x_{0},t_{0})$ to a line $gamma ={ x_{1}} imes mathbb{R}$ when coefficient $eta $ has a quadratic asymptotic behavior by means of a variational approach. |
| first_indexed | 2024-12-13T19:17:49Z |
| format | Article |
| id | doaj.art-0aa6c6413b5b41b79ad687a9d0de804c |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-13T19:17:49Z |
| publishDate | 2006-09-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-0aa6c6413b5b41b79ad687a9d0de804c2022-12-21T23:34:15ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912006-09-01200611419Light rays in static spacetimes with critical asymptotic behavior: A variational approachValeria LuisiLet $mathcal{M}=mathcal{M}_{0}imes mathbb{R}$ be a Lorentzian manifold equipped with the static metric $langle cdot ,cdot angle _{z}=langle cdot ,cdot angle -eta (x)dt^{2}$. The aim of this paper is investigating the existence of lightlike geodesics joining a point $z_{0}=(x_{0},t_{0})$ to a line $gamma ={ x_{1}} imes mathbb{R}$ when coefficient $eta $ has a quadratic asymptotic behavior by means of a variational approach.http://ejde.math.txstate.edu/Volumes/2006/114/abstr.htmlStatic spacetimelight rayquadratic asymptotic behaviorFermat principleLjusternik-Schnirelman category. |
| spellingShingle | Valeria Luisi Light rays in static spacetimes with critical asymptotic behavior: A variational approach Electronic Journal of Differential Equations Static spacetime light ray quadratic asymptotic behavior Fermat principle Ljusternik-Schnirelman category. |
| title | Light rays in static spacetimes with critical asymptotic behavior: A variational approach |
| title_full | Light rays in static spacetimes with critical asymptotic behavior: A variational approach |
| title_fullStr | Light rays in static spacetimes with critical asymptotic behavior: A variational approach |
| title_full_unstemmed | Light rays in static spacetimes with critical asymptotic behavior: A variational approach |
| title_short | Light rays in static spacetimes with critical asymptotic behavior: A variational approach |
| title_sort | light rays in static spacetimes with critical asymptotic behavior a variational approach |
| topic | Static spacetime light ray quadratic asymptotic behavior Fermat principle Ljusternik-Schnirelman category. |
| url | http://ejde.math.txstate.edu/Volumes/2006/114/abstr.html |
| work_keys_str_mv | AT valerialuisi lightraysinstaticspacetimeswithcriticalasymptoticbehavioravariationalapproach |