Abstract
The gravitational field of an isolated, axisymmetric flat disk of spinning dust is calculated approximatively in the weak-field limit of quasi-metric gravity. Boundary conditions single out the exponential disk as a “preferred” physical surface density profile. Moreover, collective properties of the disk, in the form of an extra “induced associated” surface density playing the role of “dark matter” also emerge. Taken as an idealized model of spiral galaxy thin disks, it is shown that including this “dark matter” into the model as a gravitating source yields asymptotically flat rotation curves and a correspondence with MOND.
Similar content being viewed by others
References
A. Aguirre, C.P. Burgess, A. Friedland, D. Nolte, Class. Quantum Grav. 18, R223 (2001)
D. Østvang, Gravit. Cosmol. 11, 205 (2005) gr-qc/0112025
D. Østvang, Doctoral thesis (NTNU, Trondheim, 2001) gr-qc/0111110
D. Østvang, Gravit. Cosmol. 13, 1 (2007) gr-qc/0201097
D. Østvang, Acta Phys. Pol. B 39, 1849 (2008) gr-qc/0510085
A. Toomre, Astrophys. J. 138, 385 (1963)
J. Binney, S. Tremaine, Galactic dynamics (Princeton University Press, Princeton, NJ, 1987)
M. Abramowitz, I.A. Stegun, Handbook of mathematical functions (Dover Publications Inc., New York, 1972)
A.J. Jerri, Integral and discrete transformations with applications and error analysis (Marcel Dekker Inc., New York, 1992)
G.N. Watson, J. London Math. Soc. 8, 289 (1933)
S.S. McGaugh, Astrophys. J. 632, 859 (2005)
H. Flores et al., Astron. Astrophys. 455, 107 (2006) astro-ph/0603563
M. Puech et al., Astron. Astrophys. 510, A68 (2010) arXiv:0903.3961
S.S. McGaugh, J. Wolf, Astrophys. J. 722, 248 (2010) arXiv:1003.3448
A. Romanowsky et al., Science 301, 1696 (2003)
T. Bridges et al., Mon. Not. R. Acad. Sci. 373, 157 (2006)
D. Clowe et al., Astrophys. J. 648, L109 (2006) astro-ph/0608407
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Østvang, D. Dark matter explanation from quasi-metric gravity. Eur. Phys. J. Plus 128, 75 (2013). https://doi.org/10.1140/epjp/i2013-13075-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2013-13075-3