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      Can local bulk effects explain the galactic dark matter?

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          Abstract

          We obtain the virial theorem within the context of a brane-world model without mirror symmetry or any form of junction condition. Taking a constant curvature bulk (neglecting non-local bulk effects), the local bulk effects generate a geometrical mass, contributing to the gravitational energy which may be used to explain the virial mass discrepancy in clusters of galaxies. We fix the parameter of this model in agreement with observational data.

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          An Alternative to Compactification

          Conventional wisdom states that Newton's force law implies only four non-compact dimensions. We demonstrate that this is not necessarily true in the presence of a non-factorizable background geometry. The specific example we study is a single 3-brane embedded in five dimensions. We show that even without a gap in the Kaluza-Klein spectrum, four-dimensional Newtonian and general relativistic gravity is reproduced to more than adequate precision.
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            Braneworld gravitational collapse from a radiative bulk

            We study the fate of a collapsing star on the brane in a generalized braneworld gravity with bulk matter. Specifically, we investigate for the possibility of having a static exterior for a collapsing star in the radiative bulk scenario. Here, the nonlocal correction due to bulk matter is manifest in an induced mass that adds up to the physical mass of the star resulting in an effective mass. A Schwarzschild solution for the exterior in terms of this effective mass is obtained, which reveals that even if the star exchanges energy with the bulk, the exterior may appear to be static to a braneworld observer located outside the collapsing region. The possible explanation of the situation from the discussion on the role of bulk matter is provided. The nature of bulk matter and the corresponding bulk geometry have also been obtained and analyzed, which gives a complete picture of both brane and bulk viewpoints.
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              Spherically symmetric problem on the brane and galactic rotation curves

              We investigate the braneworld model with induced gravity to clarify the role of the cross-over length scale \ell in the possible explanation of the dark-matter phenomenon in astrophysics and in cosmology. Observations of the 21 cm line from neutral hydrogen clouds in spiral galaxies reveal that the rotational velocities remain nearly constant at a value v_c ~ 10^{-3}--10^{-4} in the units of the speed of light in the region of the galactic halo. Using the smallness of v_c, we develop a perturbative scheme for reconstructing the metric in a galactic halo. In the leading order of expansion in v_c, at the distances r \gtrsim v_c \ell, our result reproduces that obtained in the Randall-Sundrum braneworld model. This inequality is satisfied in a real spiral galaxy such as our Milky Way for distances r ~ 3 kpc, at which the rotational velocity curve becomes flat, v_c ~ 7 \times 10^{-4}, if \ell \lesssim 2 Mpc. The gravitational situation in this case can be approximately described by the Einstein equations with the so-called Weyl fluid playing the role of dark matter. In the region near the gravitating body, we derive a closed system of equations for static spherically symmetric situation under the approximation of zero anisotropic stress of the Weyl fluid. We find the Schwarzschild metric to be an approximate vacuum solution of these equations at distances r \lesssim (r_g \ell^2)^{1/3}. The value \ell \lesssim 2 Mpc complies well with the solar-system tests. At the same time, in cosmology, a low-density braneworld with \ell of this order of magnitude can mimic the expansion properties of the high-density LCDM (lambda + cold dark matter) universe at late times. Combined observations of galactic rotation curves and gravitational lensing can possibly discriminate between the higher-dimensional effects and dark matter.
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                Author and article information

                Journal
                18 August 2008
                Article
                10.1088/1475-7516/2008/08/018
                0808.2335
                077e9029-0c72-4bb8-a34a-16bc8d075c15

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                JCAP 0808:018,2008
                11 pages, no figures
                gr-qc hep-th

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