Estudo de objetos compactos em um universo com constante cosmológica

Abstract

This thesis aims at modeling compact objects, either in a static configuration, ide ally simulating neutron stars, or collapsing, which may result in a black hole. For this, we consider a radiant fluid in gravitational collapse with radial heat flow, bulk viscosity, and anisotropic pressures in a space-time with cosmological constant. Although we were unable to integrate the equation that would allow us to study analytically all the relevant physical quantities, during the collapse process, these quantities are presented in terms of a function of time, which determines such evolution. As an alternative, we analyze the particular cases where the radial pressure is zero and, in another approach, we investigate the influence of the cosmological constant in a linear approximation. A solution of Einstein’s field equations with temporal dependence was presented, with relevant physical quantities being studied, such as the mass-energy function and luminosity for an observer at infinity. We also analyzed the static case with cosmological constant, where two density profiles (STEWART, 1982) (DURGAPAL; BANNERJI, 1983) proposed in the literature to model neutron stars were considered. For them, a non-local equation of state with a cosmological constant is obtained as a consequence of the chosen metric. In these cases, the energy conditions were analyzed in order to ensure the physical reasonableness of the models. Stewart’s profile admits the presence of dark energy inside the object in the outermost layers for certain ranges of the mass-radius ratio γ. There are also values of γ where all energy conditions are satisfied. The Durgapal-Bannerji profile does not allow dark energy, and in order to ensure that all energy conditions are fulfilled for a specific range of γ, it only allows solutions for Λ < 0. In another direction, we also investigate the case in which radial pressure is zero. It reveals that the negative cosmological constantcan compensate for the absence of radial pressure.