Impacto da equação de estado nas propriedades de cascas auto-gravitantes

Abstract

The study of self-gravitating shells has had a great growth in recent years, because its exploration can clarify the thermodynamic characteristics intrinsic to the gravitational field and, in turn, provide us with useful physical guidelines in the search for a quantum description of space- time. This happens because shells are the simplest theoretical objects that can be thought of as solutions to a given gravitational theory that describes two regions of space-time separated by an infinitely thin region where matter is confined. Such a system combines the notions of vacuum, typical of black holes, with the presence of matter, which can be described by means of statistical mechanics and thermodynamics, through the junction relations between the space-times internal and external to the shell, it is possible to obtain the hydrostatic equilibrium equation, which combined with a microscopic state equation for matter, allows the calculation of the mass-radius relationship of these objects. In this work, a shell is studied whose interior it is a flat space-time, described by Minkowski geometry and its exterior is a curved space-time, described by Schwarzschild geometry. Several equations of state in two spatial dimensions are used to describe the shell matter, all of nuclear degrees of freedom: free neutron gas, free neutron gas, protons and electrons, interacting nuclear matter, modeled using Walecka linear and non-linear and finally a free quarks gas. The mechanical stability of these objects in the face of radial disturbances is also studied.