Introdução à relatividade geral e à solução numérica de modelos para estrelas politrópicas

Abstract

Theobjectiveofthisworkistodevelopprogramstomodelofrelativisticandnon-relativistic politropic stars, using the Runge-Kutta-Fehlberg method. A concise and accessible general relativity introductory material for students of the last years of licentiate in physics was presented. It was developed a detailed solution of the field equations of Einstein to an matter-energy distribution of static and spherically symmetric, giving rise to the TolmanOppenheimer-Volkoff equation. The implementation of the Runge-Kutta-Fehlberg method inthesolutionofthemodelsforrelativisticandnon-relativisticpolitropicsstarswasshowed in details. Simulations of the non-relativistic polytropic star model for polytopic indexes n = 0, n = 1, n = 3, and n = 5 were compared to literature results. Simulations of the relativistic polytopic star model for polytopic indexes n =0.1, n =0.2, n =0.3, n =0.4, n =0.5, n =0.6, n =0.7, n =0.8, n =0.9, n =1 and n =3 were compared with results from the literature. Systems of differential equations of the relativistic and non-relativistic polytopic star models for polytopic index n = 1.5, K = 5.3802×103Nm3/kg5/3 and centraldensityrangingfrom1×1016kg/m3 to1×1020kg/m3 weresolvedbyRunge-KuttaFehlberg method with maximum space step of hmax =1×10−5, space step minimum of hmin =1×10−15 and tolerance of tol =1×10−6.