[Paper Review] Black Holes in String Theory

Juan Maldacena|ArXiv.org|Jul 31, 1996

Black Holes and Theoretical Physics15 references183 citations

TL;DR

This paper provides a microscopic quantum description of black holes in string theory by counting D-brane states, successfully reproducing the Bekenstein-Hawking entropy for extremal and near-extremal black holes in five and four dimensions. Using D-brane configurations and weak-coupling calculations, it demonstrates that entropy arises from counting degenerate quantum states, and confirms the Hawking temperature and radiation rate through string dynamics, supporting unitary black hole evaporation.

ABSTRACT

This thesis is devoted to trying to find a microscopic quantum description of black holes. We consider black holes in string theory which is a quantum theory of gravity. We find that the ``area law'' black hole entropy for extremal and near-extremal charged black holes arises from counting microscopic configurations. We study black holes in five and four spacetime dimensions. We calculate the Hawking temperature and give a physical picture of the Hawking decay process. Hopefully, the reader will find here a moderately self contained review of D-branes and string theory applied to black hole physics.

Motivation & Objective

• To resolve the black hole information paradox by constructing a unitary quantum description of black hole evaporation.
• To provide a microscopic statistical origin for the Bekenstein-Hawking entropy of extremal and near-extremal black holes.
• To demonstrate that D-brane configurations in string theory can account for the thermodynamic properties of black holes, including entropy and temperature.
• To test whether string theory's non-perturbative solitons (D-branes) fully describe black hole degrees of freedom beyond perturbation theory.
• To explore whether the D-brane framework correctly captures the Hawking radiation process and its dependence on black hole geometry.

Proposed method

• Use of D-branes as non-perturbative solitons in string theory to model charged black holes in five and four spacetime dimensions.
• Application of U-duality to relate different brane configurations and map them to black hole solutions with fixed mass and charge.
• Counting of degenerate quantum ground states of BPS-saturated D-brane systems to compute entropy in the weak-coupling regime.
• Comparison of the entropy from D-brane state counting with the classical Bekenstein-Hawking area law to verify agreement.
• Modeling Hawking radiation as the decay of open strings on D-branes into closed strings, with the rate proportional to the black hole horizon area.
• Use of effective string theory and open string dynamics to compute the Hawking temperature and radiation spectrum, matching classical results.

Experimental results

Research questions

• RQ1 Can the Bekenstein-Hawking entropy of extremal and near-extremal black holes be microscopically accounted for by counting D-brane states in string theory?
• RQ2 Does the D-brane description of black holes reproduce the correct Hawking temperature and radiation rate?
• RQ3 How does the entropy of black holes in N=8 supergravity compactified on a six-torus relate to the degeneracy of D-brane and D-brane-antibrane configurations?
• RQ4 To what extent do D-branes account for all non-perturbative degrees of freedom necessary to describe black hole thermodynamics?
• RQ5 Can the D-brane framework describe the dynamics of black hole formation and evaporation in a unitary quantum mechanical way?

Key findings

• The entropy of extremal and near-extremal black holes in five and four dimensions is successfully reproduced by counting the degeneracy of D-brane and D-brane-antibrane configurations in the weak-coupling limit.
• The D-brane state counting yields an entropy that matches the classical Bekenstein-Hawking area law, confirming the statistical origin of black hole entropy.
• The Hawking temperature derived from D-brane dynamics agrees precisely with the classical result, validating the thermodynamic picture.
• Hawking radiation is described as the decay of open strings on D-branes into closed strings, with the emission rate proportional to the black hole horizon area.
• The absorption cross-section for radiation modes is found to be proportional to the area, indicating that the D-brane model encodes geometric information.
• The energy gap for excitations of extremal black holes matches between the classical and D-brane descriptions, supporting consistency across scales.