Braneless Black Holes

TL;DR

This paper argues that, in the fat black hole regime, a string-based description with an effectively rescaled tension due to gravitational redshift better accounts for entropy than naive D-brane constructions. By linking the Rindler energy to the string oscillator level and treating the near-horizon region as Rindler space, the authors derive an entropy formula of the form $S = 2\pi\sqrt{c/6}\;E_R$ with $c=6$, which reproduces the Schwarzschild entropy across dimensions when $E_R \sim \sqrt{N}$. The analysis is demonstrated explicitly for a 5D black hole and extended to Schwarzschild black holes in $D$ dimensions, showing that the Hawking temperature aligns with the redshifted Hagedorn temperature of the effective string scale. A complementary discussion connects entropy to a universal density of string segments on the horizon, suggesting a horizon-filling, string-length- based microscopic picture that applies beyond specific D-brane configurations.

Abstract

It is known that the naive version of D-brane theory is inadequate to explain the black hole entropy in the limit in which the Schwarzschild radius becomes larger than all compactification radii. We present evidence that a more consistent description can be given in terms of strings with rescaled tensions. We show that the rescaling can be interpreted as a redshift of the tension of a fundamental string in the gravitational field of the black hole. An interesting connection is found between the string level number and the Rindler energy. Using this connection, we reproduce the entropies of Schwarzschild black holes in arbitrary dimensions in terms of the entropy of a single string at the Hagedorn temperature.