The long string at the stretched horizon and the entropy of large non-extremal black holes

Abstract

Highly excited or high-temperature string gases are dominated by long strings. The avatar of this process on the thermal manifold is the singly wound state (thermal scalar) that becomes massless at the critical Hagedorn temperature. This logic can be extended to curved spacetime, and in particular to Rindler space where one finds that the Hagedorn temperature equals the Hawking temperature of the black hole itself. This results in a long random walk surrounding the event horizon localized at string length distance. Long strings also make their appearance when throwing in strings into the black hole as shown by Susskind long ago. The string elongates as it approaches the horizon. We combine and compare these two pictures to discuss how the thermally equilibrated long string gas accounts for the black hole entropy, and provide a qualitative picture for Hawking radiation.