Quantum black holes

It is often said that quantum mechanics and gravity are incompatible. Recent progress in string theory has changed this perspective, showing that they are actually intertwined in a deep and surprising way, making them instead inseparable! This progress originated from the realization that black holes are quantum objects, which eventually led to the holographic principle and the view of gravity as emerging from quantum mechanics. In this thesis, we explore some aspects of these ideas by investigating quantum black holes. We first study the holographic principle and its application to near extreme black holes, with a special focus on the Kerr geometry. We then examine quantum corrections to black hole entropy, emphasizing the universality of the logarithmic corrections. We finally explore the relation between entanglement and geometry by attempting to construct a wormhole that is eternally traversable.