<p>In this thesis, we consider two different problems relevant to general relativity. Overthe last few years, opinions on physically relevant singularities occurring in FRWcosmologies have considerably changed. We present an extensive catalogue of suchcosmological milestones using generalized power series both at the kinematical anddynamical level. We define the notion of “scale factor singularity” and explore its relationto polynomial and differential curvature singularities. We also extract dynamicalinformation using the Friedmann equations and derive necessary and sufficient conditionsfor the existence of cosmological milestones such as big bangs, big crunches, bigrips, sudden singularities and extremality events. Specifically, we provide a completecharacterization of cosmological milestones for which the dominant energy conditionis satisfied. The second problem looks at one of the very small number of seriousalternatives to the usual concept of an astrophysical black hole, that is, the gravastarmodel developed by Mazur and Mottola. By considering a generalized class of similarmodels with continuous pressure (no infinitesimally thin shells) and negative centralpressure, we demonstrate that gravastars cannot be perfect fluid spheres: anisotropcpressures are unavoidable. We provide bounds on the necessary anisotropic pressureand show that these transverse stresses that support a gravastar permit a higher compactnessthan is given by the Buchdahl–Bondi bound for perfect fluid stars. We alsocomment on the qualitative features of the equation of state that such gravastar-likeobjects without any horizon must have.</p>
Junction conditions and thin shells in perfect-fluid
f(R,T)
gravity
