I will argue that the recently introduced quasilocal framework for black hole mechanics (based on the form of the near horizon geometry of stationary black holes (BHs)) together with an additional assumption on the degeneracy of the area spectrum in quantum gravity (holography for non geometric degrees of freedom) leads to agreement between the statistical mechanical treatment of quantum black holes and standard semiclassical results in BH thermodynamics. More precisely, up to small quantum corrections, quantum black holes satisfy the following properties: Entropy is Bekenstein-Hawking entropy, and fluctuations of the horizon area are small. Moreover, under the above assumption, an explicit correspondence between the statistical mechanical treatment of the fundamental LQG degrees of freedom and the semiclassical Euclidean path integral formulation can be explicitly established.
In this talk, I will briefly review the main ingredients of the gravitational asymptotic safety program before focusing on the phenomenological consequences originating from the scale-dependent couplings characteristic for the theory. In particular, I will discuss recent unexpected developments in unveiling the structure of microscopic black holes within Asymptotic Safety: in the asymptotic UV the structure of the quantum solutions is universal and given by the classical Schwarzschild-de Sitter solution, entailing a self-similarity between the classical and quantum regime. As a consequence asymptotically safe black holes evaporate completely and no Planck-size remnants are formed. The relation of these results to previous criticism that Asymptotic Safety does not reproduce the state-count of a conformal field theory will be addressed.
I will give an introduction to the geometric aspects of Lie algebroids and show how they give the correct framework to discuss gauge theories. The analysis is solely based on geometry, and thus applies to every gauge theory, independently of their specific features and dynamics. By thoroughly re-formulating the physical content of gauge theories on Atiyah Lie algebroids, we will show that the BRST construction is part of the formalism, indicating a fascinating interplay between classical geometry and quantum physics. Time permitting, we will show how our setup encompasses gravitational theories too, once the frame bundle and solder form are added to the picture.