The Fuzzball Paradigm

We describe the puzzles that arise in the quantum theory of black holes, and explain how they are resolved in string theory. We review how the Bekenstein entropy is obtained through the count of brane bound states. We describe the fuzzball construction of black hole microstates. These states have no horizon and radiate from their surface like a normal body, so there is no information puzzle. We explain how the semiclassical approximation is violated in gravitational collapse even though curvatures are low at the classical horizon. This violation happens because the collapse leads to a stretching of space that is {\it fast}: light does not have time to travel across the collapsing region to establish the `vecro' correlations needed in the quantum gravitational vacuum. These vecro correlations arise from the existence of virtual fuzzball fluctuations in the gravitational vacuum, and are significant because of the large degeneracy of fuzzball states implied by the Bekenstein entropy. It is plausible that similar effects of fast expansion may be responsible for effects like dark energy and the Early Dark Energy postulated to explain the Hubble tension.