Black hole entropy and long strings

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