Black Hole Entropy in Canonical Quantum Gravity and Superstring Theory

TL;DR

The paper investigates black hole entropy in the infinite-mass limit using both canonical quantum gravity and superstring theory. It shows that quantum-field divergences near the horizon are equivalent to renormalization of the gravitational coupling G, rendering the entropy finite only if G is finite, as in string theory. String theory identifies horizon-bound string states (open strings with ends on the horizon) as the microstates counted by the entropy, yielding a finite σ/A = 1/(4G_R) to all orders in perturbation theory. Two-dimensional models fail to capture the correct renormalization structure, reinforcing the need for a full four-dimensional string-theoretic treatment. Overall, the work argues that black hole information is encoded in horizon microstates and that string theory provides a consistent, finite accounting of black hole entropy.

Abstract

In this paper the entropy of an eternal Schwarzschild black hole is studied in the limit of infinite black hole mass. The problem is addressed from the point of view of both canonical quantum gravity and superstring theory. The entropy per unit area of a free scalar field propagating in a fixed black hole background is shown to be quadratically divergent near the horizon. It is shown that such quantum corrections to the entropy per unit area are equivalent to the quantum corrections to the gravitational coupling. Unlike field theory, superstring theory provides a set of identifiable configurations which give rise to the classical contribution to the entropy per unit area. These configurations can be understood as open superstrings with both ends attached to the horizon. The entropy per unit area is shown to be finite to all orders in superstring perturbation theory. The importance of these conclusions to the resolution of the problem of black hole information loss is reiterated.