Thin-disk models in an integrable Weyl–Dirac theory
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- 作者：Ronaldo S. S. Vieira (1)
Patricio S. Letelier (2) - 关键词：Weyl–Dirac theory ; Exact solutions ; Galaxy astrophysics ; Modified gravity
- 刊名：General Relativity and Gravitation
- 出版年：2014
- 出版时间：January 2014
- 年：2014
- 卷：46
- 期：1
- 全文大小：312 KB
- 参考文献：1. Binney, J., Tremaine, S.: Galactic Dynamics, 2nd ed. Princeton University Press, Princeton (2008)
2. Karas, V., Huré, J.-M., Semerák, O.: Gravitating discs around black holes. Class. Quantum Gravity <strong class="a-plus-plus">21strong>, R1 (2004) ss="external" href="http://dx.doi.org/10.1088/0264-9381/21/7/R01" target="_blank" title="It opens in new window">CrossRef
3. Semerák, O.: Towards Gravitating Discs Around Stationary Black Holes. arXiv:gr-qc/0204025
4. Bonnor, W.A., Sackfield, A.: The interpretation of some spheroidal metrics. Comm. Math. Phys. <strong class="a-plus-plus">8strong>, 338 (1968) ss="external" href="http://dx.doi.org/10.1007/BF01646273" target="_blank" title="It opens in new window">CrossRef
5. Morgan, T., Morgan, L.: The gravitational field of a disk. Phys. Rev. <strong class="a-plus-plus">183strong>, 1097 (1969) ss="external" href="http://dx.doi.org/10.1103/PhysRev.183.1097" target="_blank" title="It opens in new window">CrossRef
6. Morgan, L., Morgan, T.: Gravitational field of shells and disks in general relativity. Phys. Rev. D <strong class="a-plus-plus">2strong>, 2756 (1970) ss="external" href="http://dx.doi.org/10.1103/PhysRevD.2.2756" target="_blank" title="It opens in new window">CrossRef
7. Bi?ák, J., Lynden-Bell, D., Katz, J.: Relativistic disks as sources of static vacuum spacetimes. Phys. Rev. D <strong class="a-plus-plus">47strong>, 4334 (1993) ss="external" href="http://dx.doi.org/10.1103/PhysRevD.47.4334" target="_blank" title="It opens in new window">CrossRef
8. Vogt, D., Letelier, P.S.: Exact general relativistic perfect fluid disks with halos. Phys. Rev. D <strong class="a-plus-plus">68strong>, 084010 (2003) ss="external" href="http://dx.doi.org/10.1103/PhysRevD.68.084010" target="_blank" title="It opens in new window">CrossRef
9. Coimbra-Araújo, C.H., Letelier, P.S.: A thin disk in higher-dimensional space-time and dark matter interpretation. Phys. Rev. D <strong class="a-plus-plus">76strong>, 043522 (2007) ss="external" href="http://dx.doi.org/10.1103/PhysRevD.76.043522" target="_blank" title="It opens in new window">CrossRef
10. Miyamoto, M., Nagai, R.: Three-dimensional models for the distribution of mass in galaxies. Publ. Astron. Soc. Jpn. <strong class="a-plus-plus">27strong>, 533 (1975)
11. González, G.A., Letelier, P.S.: Exact general relativistic thick disks. Phys. Rev. D <strong class="a-plus-plus">69strong>, 044013 (2004) ss="external" href="http://dx.doi.org/10.1103/PhysRevD.69.044013" target="_blank" title="It opens in new window">CrossRef
12. Vogt, D., Letelier, P.S.: Relativistic models of galaxies. Mon. Not. R. Astron. Soc. <strong class="a-plus-plus">363strong>, 268-84 (2005) ss="external" href="http://dx.doi.org/10.1111/j.1365-2966.2005.09436.x" target="_blank" title="It opens in new window">CrossRef
13. Coimbra-Araújo, C.H., Letelier, P.S.: Gravity with extra dimensions and dark matter interpretation: phenomenological example via Miyamoto–Nagai galaxy. Braz. J. Phys. <strong class="a-plus-plus">42strong>, 100 (2012) ss="external" href="http://dx.doi.org/10.1007/s13538-012-0059-0" target="_blank" title="It opens in new window">CrossRef
14. Begeman, K.G.: HI Rotation Curves of Spiral Galaxies. PhD. Thesis, Rijksuniversiteit Groningen (1987)
15. Begeman, K.G.: HI rotation curves of spiral galaxies—I.NGC3198. Astron. Astrophys. <strong class="a-plus-plus">223strong>, 47-0 (1989)
16. de Blok, W.J.G., McGaugh, S.S., Rubin, V.: High-resolution rotation curves of Low Surface Brightness galaxies—II. Mass models. Astrophys. J. <strong class="a-plus-plus">122strong>, 2396-427 (2001)
17. de Blok, W.J.G., McGaugh, S.S.: The dark and visible matter content of low surface brightness disc galaxies. Mon. Not. R. Astron. Soc. <strong class="a-plus-plus">290strong>, 533 (1997) ss="external" href="http://dx.doi.org/10.1093/mnras/290.3.533" target="_blank" title="It opens in new window">CrossRef
18. Zurita, A., Rela?o, M., Beckman, J.E., Knapen, J.H.: Ionized gas kinematics and massive star formation in NGC 1530. Astron. Astrophys. <strong class="a-plus-plus">413strong>, 73 (2004) ss="external" href="http://dx.doi.org/10.1051/0004-6361:20031049" target="_blank" title="It opens in new window">CrossRef
19. de Blok, W.J.G.: The core-cusp problem. Adv. Astron. <strong class="a-plus-plus">2010strong>, 789293 (2010)
20. Navarro, J.F., Frenk, C.S., White, S.D.M.: The structure of cold dark matter halos. Astrophys. J. <strong class="a-plus-plus">462strong>, 563 (1996) ss="external" href="http://dx.doi.org/10.1086/177173" target="_blank" title="It opens in new window">CrossRef
21. Einasto, J.: Dark Matter. arXiv:0901.0632v2 [astro-ph.CO]
22. Sanders, R.H.: The Dark Matter Problem: A Historical Perspective. Cambridge University Press, Cambridge (2010)
23. Rodrigues, D.C., Letelier, P.S., Shapiro, I.L.: Galaxy rotation curves from general relativity with renormalization group corrections. JCAP <strong class="a-plus-plus">04strong>, 020 (2010) ss="external" href="http://dx.doi.org/10.1088/1475-7516/2010/04/020" target="_blank" title="It opens in new window">CrossRef
24. Brownstein, J.R., Moffat, J.W.: Galaxy rotation curves without nonbaryonic dark matter. Astrophys. J. <strong class="a-plus-plus">636strong>, 721-41 (2006) ss="external" href="http://dx.doi.org/10.1086/498208" target="_blank" title="It opens in new window">CrossRef
25. Sanders, R.H., McGaugh, S.S.: Modified Newtonian dynamics as an alternative to dark matter. Ann. Rev. Astron. Astrophys. <strong class="a-plus-plus">40strong>, 263-17 (2002) ss="external" href="http://dx.doi.org/10.1146/annurev.astro.40.060401.093923" target="_blank" title="It opens in new window">CrossRef
26. Weyl, H.: Gravitation and electricity. In: O’Rafeartaigh (ed.) The Dawning of Gauge Theory, pp. 24-7. Princeton University Press, Princeton (1997)
27. Dirac, P.A.M.: Long range forces and broken symmetries. Proc. R. Soc. Lond. A <strong class="a-plus-plus">333strong>, 403-18 (1973)
28. Canuto, V., Adams, P.J., Hsieh, S.-H., Tsiang, E.: Scale-covariant theory of gravitation and astrophysical applications. Phys. Rev. D <strong class="a-plus-plus">16strong>(6), 1643-663 (1977) ss="external" href="http://dx.doi.org/10.1103/PhysRevD.16.1643" target="_blank" title="It opens in new window">CrossRef
29. Israelit, M.: Matter creation by geometry in an integrable Weyl–Dirac theory. Found. Phys. <strong class="a-plus-plus">29strong>, 1303 (1999) ss="external" href="http://dx.doi.org/10.1023/A:1018811915703" target="_blank" title="It opens in new window">CrossRef
30. Carroll, R.: Remarks on Weyl Geometry and Quantum Mechanics. arXiv:0705.3921v3 [gr-qc]
31. Israelit, M.: Primary matter creation in a Weyl–Dirac cosmological model. Found. Phys. <strong class="a-plus-plus">32strong>, 295 (2002) ss="external" href="http://dx.doi.org/10.1023/A:1014465327475" target="_blank" title="It opens in new window">CrossRef
32. Israelit, M.: Quintessence and dark matter created by Weyl–Dirac geometry. Found. Phys. <strong class="a-plus-plus">32strong>, 945 (2002) ss="external" href="http://dx.doi.org/10.1023/A:1016063430245" target="_blank" title="It opens in new window">CrossRef
33. Israelit, M.: A Weyl–Dirac cosmological model with DM and DE. Gen. Relativ. Gravit. <strong class="a-plus-plus">43strong>, 751 (2011) ss="external" href="http://dx.doi.org/10.1007/s10714-010-1092-3" target="_blank" title="It opens in new window">CrossRef
34. Mirabotalebi, S., Jalalzadeh, S., Sadegh Movahed, M., Sepangi, H.R.: Weyl–Dirac predictions on galactic scales. Mon. Not. R. Astron. Soc. <strong class="a-plus-plus">385strong>, 986 (2008) ss="external" href="http://dx.doi.org/10.1111/j.1365-2966.2008.12904.x" target="_blank" title="It opens in new window">CrossRef
35. Letelier, P.S.: Stability of circular orbits of particles moving around black holes surrounded by axially symmetric structures. Phys. Rev. D <strong class="a-plus-plus">68strong>, 104002 (2003) ss="external" href="http://dx.doi.org/10.1103/PhysRevD.68.104002" target="_blank" title="It opens in new window">CrossRef
36. Folland, G.B.: Weyl manifolds. J. Differ. Geom. <strong class="a-plus-plus">4strong>, 145 (1970)
37. O’Neill, B.: Semi-Riemannian Geometry with Applications to Relativity. Academic Press, New York (1983)
38. Buchdahl, H.A.: Reciprocal static metrics and scalar fields in the general theory of relativity. Phys. Rev. <strong class="a-plus-plus">115strong>, 1325 (1959) ss="external" href="http://dx.doi.org/10.1103/PhysRev.115.1325" target="_blank" title="It opens in new window">CrossRef
39. Griffiths, J.B., Podolsky, J.: Exact Space-Times in Einstein’s General relativity. Cambridge University Press, Cambridge (2009)
40. Taub, A.H.: Space-times with distribution-valued curvature tensors. J. Math. Phys. <strong class="a-plus-plus">21strong>, 1423 (1980) ss="external" href="http://dx.doi.org/10.1063/1.524568" target="_blank" title="It opens in new window">CrossRef
41. Arfken, G.B., Weber, H.J.: Mathematical Methods for Physicists, 5th ed. Harcourt Academic Press, Burlington (2001)
42. Jackson, J.D.: Classical Electrodynamics, 3rd ed. Wiley, New York (1999)
43. Landau, L.D., Lifshitz, E.M.: Fluid Mechanics, Course of Theoretical Physics vol. 6, 2nd ed. Elsevier, Amsterdam (1987) - 作者单位：Ronaldo S. S. Vieira (1)
Patricio S. Letelier (2)
1. Instituto de Física “Gleb Wataghin- Universidade Estadual de Campinas, Campinas, SP, 13083-859, Brazil
2. Departamento de Matemática Aplicada-IMECC, Universidade Estadual de Campinas, Campinas, SP, 13081-970, Brazil - ISSN：1572-9532
文摘
We construct a class of static, axially symmetric solutions representing razor-thin disks of matter in the Integrable Weyl–Dirac theory proposed in Israelit (Found Phys 29:1303, 1999). The main differences between these solutions and the corresponding general relativistic one are analyzed, focusing on the behavior of physical observables (rotation curves of test particles, density and pressure profiles). We consider the case in which test particles move along Weyl geodesics. The same rotation curve can be obtained from many different solutions of the Weyl–Dirac theory, although some of these solutions present strong qualitative differences with respect to the usual general relativistic model (such as the appearance of a ring-like density profile). In particular, for typical galactic parameters all rotation curves of the Weyl–Dirac model present Keplerian fall-off. As a consequence, we conclude that a more thorough analysis of the problem requires the determination of the gauge function $\beta $ on galactic scales, as well as restrictions on the test-particle behavior under the action of the additional geometrical fields introduced by this theory.