One of the main unanswered question of modern Physics is "How does gravity behave at small scales?". The aim of this thesis is to illustrate in a comprehensive but accessible way how to look for deviations from Einstein's theory of General Relativity in this regime, looking at the simplest celestial bodies: static and spherically symmetric ones.With a conservative and bottom-up approach, at smaller scales the first corrections to the action of General Relativity are generally considered to be terms quadratic in the curvature tensors; while these modifications do not cure the inconsistency between gravity and quantum mechanics, the solutions of this theory are plausible candidates to be the first-order corrections of the classical ones.

Even with such simple modifications, a striking picture emerges from the study of isolated objects: the unique Schwarzschild solution of General Relativity is only a rare bird in the set of solutions, with non-Schwarzschild black holes, wormholes and naked singularities appearing as possible substitutes.

Tailored to graduate students and researchers entering this field, this thesis shows how to construct these new solutions from action principles, how to characterize their metric, how to study their physical properties, such as their stability or Thermodynamics, and how to look for phenomenological signatures.

Autorentext

Samuele Silveravalle was born on the 20th of December 1992 in Milan, Italy, where he received a Bachelor's degree in Physics at University of Milano Bicocca in the spring of 2015, and where he took the majority of his Master's studies in theoretical Physics. Intrigued by the Renormalization Group approach to quantum gravity, he came into contact with Alfio Bonanno of the Catania Astrophysical Observatory, contact that led him to spend seven months in Sicily to study black hole solutions in quadratic gravity for his thesis. After obtaining a Master's degree in spring 2018, he spent three months with Luciano Rezzolla's group at the Goethe University of Frankfurt studying the stability of isothermal clusters in modified gravity, and a few months working as a High School teacher in Sesto San Giovanni. In autumn 2019 he obtained a Ph.D. scholarship from TIFPA-INFN, and enrolled in the XXXV cycle of the Ph.D. program in Physics at University of Trento under the supervision of MassimilianoRinaldi. In Trento he kept working on compact object solutions in quadratic gravity, and investigated some of the effects of imposing a scale symmetry to this theory, and some aspects of Yang-Mills fields in cosmology. In June 2023 he obtained his doctoral degree with a thesis entitled "Isolated objects in quadratic gravity".