NDLI: On the dark matter as a geometric effect in $$ f (\mathcal {R})$$ gravity

Content Provider	Springer Nature Link
Author	Usman, Muhammad
Copyright Year	2016
Abstract	A mysterious type of matter is supposed to exist because the observed rotational velocity curves of particles moving around the galactic center and the expected rotational velocity curves do not match. This type of matter is called dark matter. There are also a number of proposals in the modified gravity which are alternatives to the dark matter. In this contrast, in 2008, Christian G. Böhmer, Tiberiu Harko and Francisco S.N. Lobo presented an interesting idea in Böhmer et al. (Astropart Phys 29(6):386–392, 2008) where they showed that a $$ f (\mathcal {R})$$ gravity model could actually explain dark matter to be a geometric effect only. They solved the gravitational field equations in vacuum using generic $$ f (\mathcal {R})$$ gravity model for constant velocity regions (i.e. dark matter regions around the galaxy). They found that the resulting modifications in the Einstein Hilbert Lagrangian is of the form $$\mathcal {R}^{1+m}$$ , where $$m=V_{tg}^2/c^2$$ ; $$V_{tg}$$ being the tangential velocity of the test particle moving around the galaxy in the dark matter regions and c being the speed of light. From observations it is known that $$m\approx \mathcal {O}(10^{-6})$$ (Böhmer et al. 2008; Salucci et al. in Mon Not R Astron Soc 378(1):41–47, 2007; Persic et al. in Mon Not R Astron Soc 281:27–47, 1996; Borriello and Salucci in Mon Not R Astron Soc 323(2):285–292, 2001). In this article, we perform two things (1) We show that the form of $$ f (\mathcal {R})$$ they claimed is not correct. In doing the calculations, we found that when the radial component of the metric for constant velocity regions is a constant then the exact solutions for $$ f (\mathcal {R})$$ obtained is of the form of $$\mathcal {R}^{1-\alpha }$$ which corresponds to a negative correction rather than positive claimed by the authors of Böhmer et al. (2008), where $$\alpha $$ is the function of m. (2) We also show that we can not have an analytic solution of $$f(\mathcal {R})$$ for all values of tangential velocity including the observed value of tangential velocity 200–300 km/s (Salucci et al. 2007; Persic et al. 1996; Borriello and Salucci 2001) if the radial coefficient of the metric which describes the dark matter regions is not a constant. Thus, we have to rely on the numerical solutions to get an approximate model for dark matter in $$ f (\mathcal {R})$$ gravity.
Starting Page	1
Ending Page	12
Page Count	12
File Format	PDF
ISSN	00017701
Journal	General Relativity and Gravitation
Volume Number	48
Issue Number	11
e-ISSN	15729532
Language	English
Publisher	Springer US
Publisher Date	2016-10-17
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Dark matter $$ f (\mathcal {R})$$ Gravity Theoretical, Mathematical and Computational Physics Classical and Quantum Gravitation, Relativity Theory Differential Geometry Astronomy, Astrophysics and Cosmology Quantum Physics
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy

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