Geodesic congruences and their deformations in Bertrand space-times

Kumar, Prashant; Bhattacharya, Kaushik; Sarkar, Tapobrata

doi:10.1103/physrevd.86.044028

Cited by 4 publications

(14 citation statements)

References 13 publications

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“…The fact that bigger galaxies have steeper rotational velocity curves, fits well with experimental data. 10 For n < 1, the flat region of the galactic rotation curve falls within the BST. Hence in our model, matching the galactic rotation curves will require a choice of n. In this paper, we only discuss the case n = 2.…”

Section: Introductionmentioning

confidence: 87%

“…If we demand that the matching condition of our solution does not have a thin shell at the boundary then M 0 = 1/5 and M = r b /5. If we choose a typical matching radius r b ∼ 20 kpc and then restore normal units, 11 we obtain M ∼ 10 17 M ⊙ , i.e the Schwarzschild mass of the interior region turns out to be four to five orders greater than the general mass range of heavy galaxies. If we assume matching with a thin shell at the boundary and take β = 10 −3 , i.e M 0 ∼ 1/2, the Schwarzschild mass does not change appreciably.…”

Section: Introductionmentioning

confidence: 92%

“…Of course, any realistic space-time model must satisfy the energy conditions associated with GR, and in [10], [11] it was shown that a simple class of BSTs derivable from Perlick's original work do satisfy the weak and strong energy conditions. In [4], we showed that the matter seeding the BSTs can be interpreted as galactic dark matter, 3 i.e it supports flat rotation curves.…”

Section: Introductionmentioning

confidence: 99%

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Astrophysics of Bertrand space-times

2013

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We construct a model for galactic dark matter that arises as a solution of Einstein gravity, and is a Bertrand space-time matched with an external Schwarzschild metric. This model can explain galactic rotation curves. Further, we study gravitational lensing in these space-times, and in particular we consider Einstein rings, using the strong lensing formalism of Virbhadra and Ellis. Our results are in good agreement with observational data, and indicate that under certain conditions, gravitational lensing effects from galactic dark matter may be similar to that from Schwarzschild

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Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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Astrophysics of Bertrand space-times

2013

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“…(33), and energy conditions for BSTs of the form presented in Eq. (11) have been established in [20]. It is reasonable to demand that the matter contribution to the energy density of Eq.…”

Section: Bsts In the Metric F (R) Gravity Paradigmmentioning

confidence: 99%

“…Also ν = 2M/B, and in the limit ν → 1, i.e q = 0, the Schwarzschild metric is recovered. On the other hand, the general form of the energy-momentum tensor and their relationship with the energy density and principal pressures for BSTs are as follows [20] :…”

Section: Galactic Rotation Curves and Bstsmentioning

confidence: 99%

Galactic space-times in modified theories of gravity

2015

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We study Bertrand space-times (BSTs), which have been proposed as viable models of space-times seeded by galactic dark matter, in modified theories of gravity. We first critically examine the issue of galactic rotation curves in General Relativity, and establish the usefulness of BSTs to fit experimental data in this context. We then study BSTs in metric f (R) gravity and in Brans-Dicke theories. For the former, the nature of the Newtonian potential is established, and we also compute the effective equation of state and show that it can provide good fits to some recent experimental results. For the latter, we calculate the Brans-Dicke scalar analytically in some limits and numerically in general, and find interesting constraints on the parameters of the theory. Our results provide evidence for the physical nature of Bertrand space-times in modified theories of gravity. *

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Galactic dark matter and Bertrand space-times

2013

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Bertrand space-times (BSTs) are static, spherically symmetric solutions of Einstein's equations, that admit stable, closed orbits. Starting from the fact that to a good approximation, stars in the disc or halo regions of typical galaxies move in such orbits, we propose that, under certain physical assumptions, the dark matter distribution of some low surface brightness (LSB) galaxies can seed a particular class of BSTs. In the Newtonian limit, it is shown that for flat rotation curves, our proposal leads to an analytic prediction of the Navarro-Frenk-White (NFW) dark matter profile [1]. We further show that the dark matter distribution that seeds the BST, is described by a two-fluid anisotropic model, and present its analytic solution. A new solution of the Einstein's equations, with an internal BST and an external Schwarzschild metric, is also constructed. *

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Geodesic congruences and their deformations in Bertrand space-times

Cited by 4 publications

References 13 publications

Astrophysics of Bertrand space-times

Astrophysics of Bertrand space-times

Galactic space-times in modified theories of gravity

Galactic dark matter and Bertrand space-times

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