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Covariant Loop Quantum Gravity (CLQG) is a tentative background-independentand non-perturbative theory of quantum gravity which has emerged from a numberof different research directions. Recently, this theory has been applied to theso-called Planck star model -- a particular model of stellar collapse in whichnon-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 toextract physical predictions from a background independent theory of quantumgravity, to computational problems due to a lack of systematic methods toevaluate CLQG transition amplitudes. This thesis addresses these problemsdirectly. It contains an analysis of the Planck star model within the frameworkof CLQG, including a clarifying discussion on relevant conceptual issues.Moreover, a new approximation method for CLQG transition amplitudes isdeveloped. This method allows to systematically study amplitudes in thesemi-classical regime of the theory and it sheds new light on the so-calledcosine problem.

Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity