Abstract:
In this thesis, we consider two different problems relevant to general relativity. Over
the last few years, opinions on physically relevant singularities occurring in FRW
cosmologies have considerably changed. We present an extensive catalogue of such
cosmological milestones using generalized power series both at the kinematical and
dynamical level. We define the notion of “scale factor singularity” and explore its relation
to polynomial and differential curvature singularities. We also extract dynamical
information using the Friedmann equations and derive necessary and sufficient conditions
for the existence of cosmological milestones such as big bangs, big crunches, big
rips, sudden singularities and extremality events. Specifically, we provide a complete
characterization of cosmological milestones for which the dominant energy condition
is satisfied. The second problem looks at one of the very small number of serious
alternatives to the usual concept of an astrophysical black hole, that is, the gravastar
model developed by Mazur and Mottola. By considering a generalized class of similar
models with continuous pressure (no infinitesimally thin shells) and negative central
pressure, we demonstrate that gravastars cannot be perfect fluid spheres: anisotropc
pressures are unavoidable. We provide bounds on the necessary anisotropic pressure
and show that these transverse stresses that support a gravastar permit a higher compactness
than is given by the Buchdahl–Bondi bound for perfect fluid stars. We also
comment on the qualitative features of the equation of state that such gravastar-like
objects without any horizon must have.
