Bootstrapped Newtonian gravity

The aim of this thesis is to entertain the possibility of a quantum departure from the general relativistic description of compact sources in strong field regime and claim that a quantum understanding of the classical background could be necessary. We therefore develop an effective field theory providing a simplified framework to address the effects of non-linearities in strong gravitational backgrounds. Starting from a massless Fierz- Pauli-type lagrangian for the Newtonian potential and introducing the self-coupling terms, we arrive at a non-linear equation describing the effective gravitational potential of an arbitrarily compact homogeneous source. Unlike the general relativistic solutions no Buchdahl limit is found as the solutions display a regular behaviour in any compactness regime. Moreover, we provide a quantum interpretation of these results in terms of a quantum coherent state formalism. Such an approach proves to be widely capable of accounting for classical field configurations as well as providing some collective properties of the constituent soft quanta. The latter show a good agreement with some of the crucial relations of the corpuscular model. We do not interpret this approach as a model of phenomenological relevance but better as a simplified picture aimed at capturing novel quantum feature of black holes physics.