Abstract

SAAD, A. S.; NOUH, M. I.; SHAKER, A. A.  and  KAMEL, T. M.. Approximate Analytical Solutions to the Relativistic Isothermal Gas Spheres. Rev. mex. astron. astrofis [online]. 2017, vol.53, n.2, 00008.  Epub Oct 21, 2019. ISSN 0185-1101.

In this paper we introduce a novel analytical solution to TolmanOppenheimer-Volkoff (TOV) equation, which is ultimately a hydrostatic equilibrium equation derived from general relativity in the framework of relativistic isothermal spheres. To improve the convergence radii of the obtained series solutions, a combination of an Euler-Abel transformation and a Pad´e approximation has been done. The solutions are given in the ξ-θ and ξ-ν phase planes taking into account the general relativistic effects σ = 0.1, 0.2 and 0.3. A comparison between the results obtained by the suggested approach and the numerical one indicates a good agreement, with a maximum relative error of order 10−3, which establishes the validity and accuracy of the method. The proposed procedure accelerated the power series solution about ten times that of the traditional one. An application to a neutron star is presented.

Keywords : equation of state; methods; analytical; stars; neutrón; relativistic processes.

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