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Paper   IPM / Physic / 12666
School of Physics
  Title:   Relativistic Rotation Curve for Exact Asymtotically FRW Spherical Structures and the Definition of Mass
1.  M. H. Razbin
2.  J.T. Firouzjaee
3.  R. Mansouri
  Status:   Preprint
  Year:  2012
  Supported by:  IPM
Using a general relativistic exact model for spherical structures in a cosmological background, we have calculated the test particle geodesics within the structure for different masses in order to obtain the velocity profile of stars or galaxies. Defining a Newtonian mass based on the classical dynamical relations, it turns out that the Misner-Sharp quasi-local mass is almost equal to the Newtonian one. This, however, is not the case for other general relativistic quasi-local mass definitions, which can be much smaller than the mass definition based on the classical dynamics. Therefore, based on the rotation curve, we are not in a position to relate a unique mass to a cosmological structure within general relativity even in cases of very weak gravity.

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