Black holes as collapsed polymers

Abstract

We propose that a large Schwarzschild black hole (BH) is a bound state of highly excited, long, closed strings at the Hagedorn temperature. The size of the bound state is smaller than the string random-walk scale and determined dynamically by the string attractive interactions. It is further proposed that the effective free-energy density of the bound state should be expressed as a function of its entropy density. For a macroscopic BH, the free-energy density contains only linear and quadratic terms, in analogy with that of a collapsed polymer when expressed as a function of the polymer concentration. Using the effective free energy, we derive scaling relations for the entropy, energy and size of the bound state and show that these agree with the scaling relations of the BH; in particular, with the area law for the BH entropy. The area law originates from the inverse scaling of the effective temperature with the bound-state radius. We also find that the energy density of the bound state is equal to its pressure.