Geometrical and physical interpretation of the Levi-Civita spacetime in terms of the Komar mass density
We revisit the interpretation of the cylindrically symmetric, static vacuum Levi-Civita metric, known in either Weyl, Einstein–Rosen, or Kasner-like coordinates. The Komar mass density of the infinite axis source arises through a suitable compactification procedure. The Komar mass density \mu _{K} μ...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2023
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| Sorozat: | EUROPEAN PHYSICAL JOURNAL PLUS
138 No. 5 |
| Tárgyszavak: | |
| doi: | 10.1140/epjp/s13360-023-04027-9 |
| mtmt: | 33859928 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/27276 |
| Tartalmi kivonat: | We revisit the interpretation of the cylindrically symmetric, static vacuum Levi-Civita metric, known in either Weyl, Einstein–Rosen, or Kasner-like coordinates. The Komar mass density of the infinite axis source arises through a suitable compactification procedure. The Komar mass density \mu _{K} μ K calculated in Einstein–Rosen coordinates, when employed as the metric parameter, leads to a number of advantages. It eliminates double coverages of the parameter space, vanishes in flat spacetime and when small, it corresponds to the mass density of an infinite string. After a comprehensive analysis of the local and global geometry, we proceed with the physical interpretation of the Levi-Civita spacetime. First we show that the Newtonian gravitational force is attractive and its magnitude increases monotonically with all positive \mu _{K} μ K , asymptoting to the inverse of the proper distance in the radial direction. Second, we reveal that the tidal force between nearby geodesics (hence gravity in the Einsteinian sense) attains a maximum at \mu _{K}=1/2 μ K = 1 / 2 and then decreases asymptotically to zero. Hence, from a physical point of view the Komar mass density of the Levi-Civita spacetime encompasses two contributions: Newtonian gravity and acceleration effects. An increase in \mu _{K} μ K strengthens Newtonian gravity but also drags the field lines increasingly parallel, eventually transforming Newtonian gravity through the equivalence principle into a pure acceleration field and the Levi-Civita spacetime into a flat Rindler-like spacetime. In a geometric picture the increase of \mu _{K} μ K from zero to \infty ∞ deforms the planar sections of the spacetime into ever deepening funnels, eventually degenerating into cylindrical topology in an appropriately chosen embedding. |
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| Terjedelem/Fizikai jellemzők: | 19 |
| ISSN: | 2190-5444 |