  Covariant Loop Quantum Gravity (CLQG) is a tentative background-independent
and non-perturbative theory of quantum gravity which has emerged from a number
of different research directions. Recently, this theory has been applied to the
so-called Planck star model -- a particular model of stellar collapse in which
non-perturbative quantum gravity effects play a predominant role. However,
several obstacles have impeded progress in the investigation of this scenario.
These obstacles range from conceptual issues, such as the question how to
extract physical predictions from a background independent theory of quantum
gravity, to computational problems due to a lack of systematic methods to
evaluate CLQG transition amplitudes. This thesis addresses these problems
directly. It contains an analysis of the Planck star model within the framework
of CLQG, including a clarifying discussion on relevant conceptual issues.
Moreover, a new approximation method for CLQG transition amplitudes is
developed. This method allows to systematically study amplitudes in the
semi-classical regime of the theory and it sheds new light on the so-called
cosine problem.
