Fermat Metrics
In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variatio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/8/1422 |
| _version_ | 1797521955154296832 |
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| author | Antonio Masiello |
| author_facet | Antonio Masiello |
| author_sort | Antonio Masiello |
| collection | DOAJ |
| description | In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used. Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime. Finally some possible applications to other class of spacetimes are considered. |
| first_indexed | 2024-03-10T08:20:50Z |
| format | Article |
| id | doaj.art-c3395153a1d14a7c8c0a14bd50316055 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T08:20:50Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c3395153a1d14a7c8c0a14bd503160552023-11-22T10:01:14ZengMDPI AGSymmetry2073-89942021-08-01138142210.3390/sym13081422Fermat MetricsAntonio Masiello0Department of Mechanics, Mathematics and Management, Politecnico di Bari, Via Orabona 4, 70125 Bari, ItalyIn this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used. Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime. Finally some possible applications to other class of spacetimes are considered.https://www.mdpi.com/2073-8994/13/8/1422Finsler metricsstationary spacetimesFermat principlelight rayscritical point theory |
| spellingShingle | Antonio Masiello Fermat Metrics Symmetry Finsler metrics stationary spacetimes Fermat principle light rays critical point theory |
| title | Fermat Metrics |
| title_full | Fermat Metrics |
| title_fullStr | Fermat Metrics |
| title_full_unstemmed | Fermat Metrics |
| title_short | Fermat Metrics |
| title_sort | fermat metrics |
| topic | Finsler metrics stationary spacetimes Fermat principle light rays critical point theory |
| url | https://www.mdpi.com/2073-8994/13/8/1422 |
| work_keys_str_mv | AT antoniomasiello fermatmetrics |