A Correspondence Principle for Black Holes and Strings

TL;DR

This paper proposes a correspondence principle linking black holes and strings, suggesting that when a black hole's horizon shrinks below a string scale, it transitions into a string/D-brane state with consistent entropy, explaining black hole entropy statistically.

Contribution

It formulates a correspondence principle that describes the transition from black holes to string states, providing a statistical interpretation of entropy without precise numerical coefficients.

Findings

The horizon size decreases with string coupling.

Black hole states transition to string/D-brane states at the correspondence point.

The approach reproduces the correct entropy dependence on mass and charge.

Abstract

For most black holes in string theory, the Schwarzschild radius in string units decreases as the string coupling is reduced. We formulate a correspondence principle, which states that (i) when the size of the horizon drops below the size of a string, the typical black hole state becomes a typical state of strings and D-branes with the same charges, and (ii) the mass does not change abruptly during the transition. This provides a statistical interpretation of black hole entropy. This approach does not yield the numerical coefficient, but gives the correct dependence on mass and charge in a wide range of cases, including neutral black holes.