Black hole entropy and long strings

In this paper, we discuss whether black hole entropy counts short or long-range microstates in quantum gravity. In brick wall and induced gravity models, the entropy arises due to short distance correlations across the event horizon cut off at the Planck length. However, the energy of these short range degrees of freedom is too high compared to the black hole energy. We argue that the long string phenomenon, which naturally appears in matrix quantum mechanics, resolves this issue by lowering the excitation energy per degree of freedom. This mechanism also reduces the total number of microscopic degrees of freedom in a given volume, leading to a correct estimate of the Bekenstein-Hawking formula for black hole entropy.