Geodesic Incompleteness and Partially Covariant Gravity
We study the issue of length renormalization in the context of fully covariant gravity theories as well as non-relativistic ones such as Hořava–Lifshitz gravity. The difference in their symmetry groups implies a relation among the lengths of paths in spacetime in the two types of theory. Provided th...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-05-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/7/5/126 |
| _version_ | 1797535451584659456 |
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| author | Ignatios Antoniadis Spiros Cotsakis |
| author_facet | Ignatios Antoniadis Spiros Cotsakis |
| author_sort | Ignatios Antoniadis |
| collection | DOAJ |
| description | We study the issue of length renormalization in the context of fully covariant gravity theories as well as non-relativistic ones such as Hořava–Lifshitz gravity. The difference in their symmetry groups implies a relation among the lengths of paths in spacetime in the two types of theory. Provided that certain asymptotic conditions hold, this relation allows us to transfer analytic criteria for the standard spacetime length to be finite and the Perelman length to be likewise finite, and therefore formulate conditions for geodesic incompleteness in partially covariant theories. We also discuss implications of this result for the issue of singularities in the context of such theories. |
| first_indexed | 2024-03-10T11:44:40Z |
| format | Article |
| id | doaj.art-ccb88360cc7d4771888ce68aa1e9789d |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-10T11:44:40Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-ccb88360cc7d4771888ce68aa1e9789d2023-11-21T18:11:35ZengMDPI AGUniverse2218-19972021-05-017512610.3390/universe7050126Geodesic Incompleteness and Partially Covariant GravityIgnatios Antoniadis0Spiros Cotsakis1Laboratoire de Physique Théorique et Hautes Energies—LPTHE, Sorbonne Université, CNRS 4 Place Jussieu, 75005 Paris, FranceInstitute of Gravitation and Cosmology, RUDN University, ul. Miklukho-Maklaya 6, 117198 Moscow, RussiaWe study the issue of length renormalization in the context of fully covariant gravity theories as well as non-relativistic ones such as Hořava–Lifshitz gravity. The difference in their symmetry groups implies a relation among the lengths of paths in spacetime in the two types of theory. Provided that certain asymptotic conditions hold, this relation allows us to transfer analytic criteria for the standard spacetime length to be finite and the Perelman length to be likewise finite, and therefore formulate conditions for geodesic incompleteness in partially covariant theories. We also discuss implications of this result for the issue of singularities in the context of such theories.https://www.mdpi.com/2218-1997/7/5/126Hořava–Lifshitz gravitygeodesic incompletenessgeometric flows |
| spellingShingle | Ignatios Antoniadis Spiros Cotsakis Geodesic Incompleteness and Partially Covariant Gravity Universe Hořava–Lifshitz gravity geodesic incompleteness geometric flows |
| title | Geodesic Incompleteness and Partially Covariant Gravity |
| title_full | Geodesic Incompleteness and Partially Covariant Gravity |
| title_fullStr | Geodesic Incompleteness and Partially Covariant Gravity |
| title_full_unstemmed | Geodesic Incompleteness and Partially Covariant Gravity |
| title_short | Geodesic Incompleteness and Partially Covariant Gravity |
| title_sort | geodesic incompleteness and partially covariant gravity |
| topic | Hořava–Lifshitz gravity geodesic incompleteness geometric flows |
| url | https://www.mdpi.com/2218-1997/7/5/126 |
| work_keys_str_mv | AT ignatiosantoniadis geodesicincompletenessandpartiallycovariantgravity AT spiroscotsakis geodesicincompletenessandpartiallycovariantgravity |