Brane-$f(R)$ gravity and dark matter

Abstract

The collision-free Boltzmann equation is used in the context of brane-$f(R)$ gravity to derive the virial theorem. It is shown that the virial mass is proportional to certain geometrical terms appearing in the Einstein field equations and contributes to gravitational energy and that such a geometric mass can be attributed to the virial mass discrepancy in a cluster of galaxies. In addition, the galaxy rotation curves are studied by utilizing the concept of conformal symmetry and notion of conformal Killing symmetry. The field equations may then be obtained in an exact parametric form in terms of the parameter representing the conformal factor. This provides the possibility of studying the behavior of the angular velocity of a test particle moving in a stable circular orbit. The tangential velocity can be derived as a function of the conformal factor and integration constants, resulting in a constant value at large radial distances. Relevant phenomenon such as the deflection of light passing through a region where the rotation curves are flat and the radar echo delay are also studied.

12 pages, 2 figures, to appear in PRD

References in corpus (13)

• The Universal Rotation Curve of Spiral Galaxies. II The Dark Matter Distribution out to the Virial Radius
• Solar System constraints to general f(R) gravity
• Dark energy and dark matter as curvature effects
• DGP Specteroscopy
• Generalized virial theorem in f(R) gravity
• The virial theorem and the dynamics of clusters of galaxies in the brane world models
• An $f(R)$ gravitation for galactic environments
• Galactic dark matter as a bulk effect on the brane
• Astrophysical Configurations with Background Cosmology: Probing Dark Energy at Astrophysical Scales
• Accelerating universe in $f(\mathcal{R})$ brane gravity
• Comments on "Solar System constraints to general f(R) gravity"
• The general relativistic geometry of the Navarro-Frenk-White model
• Generalized virial theorem in warped DGP brane-world

Cited by in corpus (13)

• Further matters in space-time geometry: $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ gravity
• Dark Matter From f(R,T) Gravity
• Galactic rotation curves in hybrid metric-Palatini gravity
• Slowly rotating Bose Einstein Condensate galactic dark matter halos, and their rotation curves
• Testing Bose-Einstein Condensate dark matter models with the SPARC galactic rotation curves data
• Jeans instability and turbulent gravitational collapse of Bose-Einstein Condensate dark matter halos
• Effective gravitational equations for f(R) braneworld models
• Bose-Einstein Condensate dark matter models in the presence of baryonic matter and random confining potentials
• Self-similarity in static axially symmetric relativistic fluids
• Galactic rotation curves of spiral galaxies and dark matter in f(R,T) gravity theory
• Cosmological Solutions of Chameleon Scalar Field Model
• Classical Tests of General Relativity: Probing Topologically Charged Black Holes on Brane Worlds in f(R) Bulk
• Chameleon Gravity as an Alternative to Dark Matter