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      On the problem of deformed spherical systems in Modified Newtonian Dynamics

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          Abstract

          Based on Newtonian dynamics, observations show that the luminous masses of astrophysical objects that are the size of a galaxy or larger are not enough to generate the measured motions which they supposedly determine. This is typically attributed to the existence of dark matter, which possesses mass but does not radiate (or absorb radiation). Alternatively, the mismatch can be explained if the underlying dynamics is not Newtonian. Within this conceptual scheme, Modified Newtonian Dynamics (MOND) is a successful theoretical paradigm. MOND is usually expressed in terms of a nonlinear Poisson equation, which is difficult to analyse for arbitrary matter distributions. We study the MONDian gravitational field generated by slightly non-spherically symmetric mass distributions based on the fact that both Newtonian and MONDian fields are conservative (which we refer to as the compatibility condition). As the non-relativistic version of MOND has two different formulations (AQUAL and QuMOND) and the compatibility condition can be expressed in two ways, there are four approaches to the problem in total. The method involves solving a suitably defined linear deformation potential, which generally depends on the choice of MOND interpolation function. However, for some specific form of the deformation potential, the solution is independent of the interpolation function.

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          Author and article information

          Journal
          2016-04-20
          Article
          10.3847/0004-637X/821/2/111
          1604.06279
          fbecb969-a314-450d-a817-21e44d884fd1

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

          History
          Custom metadata
          Astrophysical Journal, 821, 111 (12pp), 2016 April 20
          30 pages, 2 figures
          gr-qc astro-ph.CO

          Cosmology & Extragalactic astrophysics,General relativity & Quantum cosmology

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