Relativistic models of thin disks immersed in a Robertson-Walker type spacetime
Main Article Content
Keywords
General relativity, thin disks, exact solutions, Robertson- Walker metric.
Abstract
Using the well known “displace, cut and reflect” method used to generate disks from given solutions of Einstein field equations, we construct some relativistic models of time dependent thin disks of infinite extension made of a perfect fluid based on the Robertson-Walker metric. Two simple families of models of disks based on Robertson-Walker solutions admitting Matter and Ricci collineations are presented. We obtain disks that are in agreement with all the energy conditions.
PACS: 04.40Nr
MSC: 83C22
Downloads
Download data is not yet available.
References
[1] W. A. Bonnor and A. Sackfield, “The interpretation of some spheroidal metrics,” Commun. Math. Phys., vol. 8, pp. 338-344, Apr. 1968.
[2] T. Morgan and L. Morgan, “The Gravitacional Field of a Disk,” Phys. Rev., vol. 183, pp. 1097-1101, Apr. 1969.
[3] L. Morgan and T. Morgan, “Gravitational Field of Shells and Disks in General Relativity”, Phys. Rev. D, vol. 2, pp. 2756 - 2761, Apr. 1970.
[4] G. A. Gonzalez and P. S. Letelier, “Relativistic static thin discs with radial stress support,” Class. Quantum Grav., vol. 16, pp. 479-494, Apr. 1999.
[5] J. P. S. Lemos and P. S. Letelier, “Superposition of Morgan and Morgan discs with a Schwarzschild black hole,” Class. Quantum Grav., vol. 10, pp. L75 - L78, Apr. 1993.
[6] J. Bicák, D. Lynden-Bell, and J. Katz, “Relativistic disks as sources of static vacuum spacetimes,” Phys. Rev. D, vol. 47, pp. 4334-4343, Apr. 2003.
[7] J. Bicák and T. Ledvinka, “Relativistic disks as sources of the Kerr metric,” Phys. Rev. Lett., vol. 71, pp. 1669-1672, Apr. 1993.
[8] G. A. Gonzalez and P. S. Letelier, “Rotating relativistic thin disks,” Phys. Rev. D, vol. 62, 064025, pp. 1 - 8, Apr. 2000.
[9] T. Ledvinka, J. Bicák, and M. .Zofka, “Relativistic discs as sources of Kerr-Newman fields,” in Proc. 1999 of 8th Marcel- Grossmann Meeting in General Relativity, edited by T. Piran, World Scientific, Singapore, pp. 339-341.
[10] C. H. García-Duque and G. García-Reyes, “General magnetized Weyl solutions: disks and motion of charged particles,” Gen. Relativ. Gravit., vol. 43, pp. 3001-3032, Apr. 2011.
[11] J. Katz, J. Bicák, D. Lynden-Bell, “Disc sources for conformastationary metrics,” Class. Quantum Grav., vol. 16, pp. 4023- 4034 , Apr. 1999.
[12] J. L. Synge, Relativity: The General Theory. Amsterdam: North-Holland publishing company, 1966.
[13] C. Klein, “Exact relativistic treatment of stationary blackholedisk systems,” Phys. Rev. D, vol. 68, 027501, pp. 1-4, Apr. 2003.
[14] C. Klein, “On explicit solutions to the stationary axisymmetric Einstein-Maxwell equations describing dust disks,” Annalen der Physik, vol. 12, pp. 599-639, Apr. 2003.
[15] J. Binney and S. Tremaine, Galactic Dynamics. Princeton, New Jersey: Princeton University Press, 1987, pp. 43.
[16] P. S. Apostolopoulos and M. Tsamparlis, “Geometric Equations of State in Friedmann-Lemaître Universes Admitting Matter and Ricci Collineations,” Gen. Rel. Grav. Vol. 36, pp. 277-292, Apr. 2004.
[17] H. Stephani, D. Kramer, M. McCallum, C. Hoenselaers and E. Herlt, Exact Solutions of Einstein’s Field Equations. England: Cambridge University Press, 2003, pp. 211.
[18] Ray d’Inverno, Introducing Einstein’s Relativity: Clarendon Press, Oxford, 1998, pp.. 313-314.
[19] G. García-Reyes and G. A. González, “Electrovacuum Static Counterrotating Relativistic Dust Disks,” Phys. Rev. D, vol. 70, 104005, pp.1-6, Apr. 2004.
[2] T. Morgan and L. Morgan, “The Gravitacional Field of a Disk,” Phys. Rev., vol. 183, pp. 1097-1101, Apr. 1969.
[3] L. Morgan and T. Morgan, “Gravitational Field of Shells and Disks in General Relativity”, Phys. Rev. D, vol. 2, pp. 2756 - 2761, Apr. 1970.
[4] G. A. Gonzalez and P. S. Letelier, “Relativistic static thin discs with radial stress support,” Class. Quantum Grav., vol. 16, pp. 479-494, Apr. 1999.
[5] J. P. S. Lemos and P. S. Letelier, “Superposition of Morgan and Morgan discs with a Schwarzschild black hole,” Class. Quantum Grav., vol. 10, pp. L75 - L78, Apr. 1993.
[6] J. Bicák, D. Lynden-Bell, and J. Katz, “Relativistic disks as sources of static vacuum spacetimes,” Phys. Rev. D, vol. 47, pp. 4334-4343, Apr. 2003.
[7] J. Bicák and T. Ledvinka, “Relativistic disks as sources of the Kerr metric,” Phys. Rev. Lett., vol. 71, pp. 1669-1672, Apr. 1993.
[8] G. A. Gonzalez and P. S. Letelier, “Rotating relativistic thin disks,” Phys. Rev. D, vol. 62, 064025, pp. 1 - 8, Apr. 2000.
[9] T. Ledvinka, J. Bicák, and M. .Zofka, “Relativistic discs as sources of Kerr-Newman fields,” in Proc. 1999 of 8th Marcel- Grossmann Meeting in General Relativity, edited by T. Piran, World Scientific, Singapore, pp. 339-341.
[10] C. H. García-Duque and G. García-Reyes, “General magnetized Weyl solutions: disks and motion of charged particles,” Gen. Relativ. Gravit., vol. 43, pp. 3001-3032, Apr. 2011.
[11] J. Katz, J. Bicák, D. Lynden-Bell, “Disc sources for conformastationary metrics,” Class. Quantum Grav., vol. 16, pp. 4023- 4034 , Apr. 1999.
[12] J. L. Synge, Relativity: The General Theory. Amsterdam: North-Holland publishing company, 1966.
[13] C. Klein, “Exact relativistic treatment of stationary blackholedisk systems,” Phys. Rev. D, vol. 68, 027501, pp. 1-4, Apr. 2003.
[14] C. Klein, “On explicit solutions to the stationary axisymmetric Einstein-Maxwell equations describing dust disks,” Annalen der Physik, vol. 12, pp. 599-639, Apr. 2003.
[15] J. Binney and S. Tremaine, Galactic Dynamics. Princeton, New Jersey: Princeton University Press, 1987, pp. 43.
[16] P. S. Apostolopoulos and M. Tsamparlis, “Geometric Equations of State in Friedmann-Lemaître Universes Admitting Matter and Ricci Collineations,” Gen. Rel. Grav. Vol. 36, pp. 277-292, Apr. 2004.
[17] H. Stephani, D. Kramer, M. McCallum, C. Hoenselaers and E. Herlt, Exact Solutions of Einstein’s Field Equations. England: Cambridge University Press, 2003, pp. 211.
[18] Ray d’Inverno, Introducing Einstein’s Relativity: Clarendon Press, Oxford, 1998, pp.. 313-314.
[19] G. García-Reyes and G. A. González, “Electrovacuum Static Counterrotating Relativistic Dust Disks,” Phys. Rev. D, vol. 70, 104005, pp.1-6, Apr. 2004.
Article Sidebar
Published
Nov 5, 2013
Article Details
How to Cite
García Reyes, G., & García-Quintero, E. (2013). Relativistic models of thin disks immersed in a Robertson-Walker type spacetime. Ingeniería Y Ciencia, 9(18), 131–140. https://doi.org/10.17230/ingciecia.9.18.7
Issue
Section
Articles
Supporting Agencies
Author Biographies
Gonzalo García Reyes, Universidad Tecnológica de Pereira
PhD. en Ciencias Naturales
Edwin García-Quintero, Universidad de Antioquía
PhD. en Tecnología EléctricaAuthors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).