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Polyanin, A.D. and Zaitsev, V.F. (2003) Exact Solutions for Ordinary Differential Equations. Chapman & Hall/CRC, Boca Raton, London, New York, Washington, D.C.

has been cited by the following article:

• TITLE: Anisotropic Geodesic Fluid in Non-Comoving Spherical Coordinates

  AUTHORS: Peter Christian Stichel

  KEYWORDS: Einsteins Equations, Stationary Solution, Anisotropic Geodesic Fluid, Non-Comoving Coordinates, Spherical Symmetry, Gravitational Potential, Nonlinear Ordinary Differential Equation

  JOURNAL NAME: Journal of Modern Physics, Vol.9 No.2, January 22, 2018

  ABSTRACT: We start with a recently introduced spherically symmetric geodesic fluid model (arXiv: 1601.07030) whose energy-momentum tensor (EMT) in the comoving frame is dust-like with nontrivial energy flux. In the non-comoving energy frame (vanishing energy flux), the same EMT contains besides dust only radial pressure. We present Einstein’s equations together with the matter equations in static spherically symmetric coordinates. These equations are self-contained (four equations for four unknowns). We solve them analytically except for a resulting nonlinear ordinary differential equation (ODE) for the gravitational potential. This ODE can be rewritten as a Lienard differential equation which, however, may be transformed into a rational Abel differential equation of the first kind. Finally, we list some open mathematical problems and outline possible physical applications (galactic halos, dark energy stars) and related open problems.