The End STate of GRavitational collapse: black holes or else?

General relativity (GR) is a very elegant theory from the conceptual point of view and a very successful one from the experimental side. However, there are several conceptual reasons, such as the singularity problem, that motivate the study of extensions of GR. Thestudy of black hole physics will play a pivotal role in the understanding of new physics beyond general relativity. In fact, black holes hide in their interior theoretical evidence of the breakdown of GR and they are compact objects where strong gravity effects arenonnegligible. The research proposal ""The End STate of GRavitational collapse: black holes or else? (TESTGR)"" focuses on the study of several aspects associated with the black hole singularity problem looking for possible evidence of new physics beyond GR, to understand how the modifications would manifest and how to detect them. The proposed research comprises both theoretical and phenomenological studies. It is divided into 3 working packages (WPs) that are strongly interconnected but that can be studied independently. The first WP studies the mechanism leading to the formation of black holes mimickers. The second WP addresses crucial issues related to the viability and stability of the identified classes of spacetimes. Finally, the last WP focuses on the interplay with observations.This research proposal is particularly timing as the LIGO/VIRGO/KAGRA detectors, the EHT, as well as the next generation of earth and space-based interferometers, will collect plenty of data in future years. This leads to a growing necessity for theoretical studiesbeyond general relativity to understand if the data contains evidence of new physics that can revolutionize our understanding of nature.""