Soluções das equações de campo de Einstein para fluidos perfeitos estáticos com simetria esférica

Abstract

In this work we study static perfect fluid space-times with spherical symmetry within the framework of General Relativity using a coordinate system in which the equation of pressure isotropy is a linear first-order ordinary differential equation in terms of one of the functions of the metric, and a linear second-order differential equation in the other metric function. Imposing a rational ansatz for the metric function 11 g , we obtain an ordinary differential equation for the remaining metric function which is linear, homogeneous and of second-order with rational coefficients. The ansätze proposed by us are: g11=-A/4x x-z1/x-Z1, g11=-A/4x x-z1/(x-Z1)(x-Z2), g11=-A/4x (x-z1) (x-z2)/x-Z1 and g11= -A/4x (x-z1) (x-z2)/ 4x(x-Z1) (x-Z2) where x is a spacial coordinate and 1 2 1 2 Α, z , z , Z and Z are parameters of the models. These ansätze produce exactly the type of differential equation whose closed-form liouvillian solutions, if such exist, can be found by applying Kovacic's algorithm. After applying this algorithm we verified if the solutions satisfy physical conditions which mean they could be used as models for nonrotating neutron stars, where the relativistic effects of the high density are expected to be important.