MG14 - Talk detail

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Abstract

The white dwarfs represent the endpoint of stellar evolution. They are formed when a star with mass between approximately 0.07 to 8-10 $M_\odot$, exhausts its nuclear fuel. At this point the process that sustains its stability stops. After this, the internal pressure can no longer stand the gravitational force and the star collapses. In this work we investigate the structure of these stars which are described by the equations of Tolman-Oppenheimer-Volkoff (TOV) and compare with the Newtonian equations of gravitation in order to put in evidence the importance of the General Relativity i the study of these stars. These equations show us how the pressure varies with the mass and radius of the star. We consider the TOV equations for both relativistic and non-relativistic cases for equation of state (EoS). In the case of white dwarf (WD) star the internal pressure that balances the gravitational one is essentially the pressure coming from the degeneracy of the fermions. To have solved the TOV equations we need an equation of state that shows how this internal pressure is related to the energy density. Instead of using politropic equations of state we have solved the equations numerically using the exact relativistic energy equation for the model of fermion gas at temperature $T=0$ and compared with the solutions using the politropic approaches. We also discuss the instability due to the neutronization threshold and the Coulomb corrections to the Chandrasekhar model for WDs of homogeneous composition that was performed by Hamada and Salpeter (HS) in 1961 and Rotondo, Rueda and Ruffini (RRR) in 2011. We conclude that for a given mass the HS and RRR models give a smaller radius and larger central density compared the Chandrasekhar model. Finally in our results we compute the differences in the maximum mass for WDs composed different nucleus. We also propose a fit of the numerical solution of the TOV with the general EoS for the WD mass-radius diagram. We propose that our fit has to be used as relation between mass and radius for general relativistic WDs instead of that newtonian $M\sim 1/R^3$, this fit is a new expression that we found and is given by $M=R/(a+bR+cR^2+dR^3+kR^4)$, where a, b, c and d are parameters and $1/k$ it's the constant of the non-relativistic mass-radius relation and it can be used in the simulation study of binary systems that occurs accretion.

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