[Paper Review] Quantum Aspects of Black Holes

Jeffrey A. Harvey, Andrew Strominger|arXiv (Cornell University)|Sep 16, 1992

Black Holes and Theoretical Physics39 references3 citations

TL;DR

This paper reviews quantum aspects of black holes, focusing on entropy, information paradox, and the role of string theory in resolving quantum gravity issues. It proposes that black hole entropy arises from microscopic quantum states, with the Bekenstein-Hawking formula derived from string theory in extremal black hole limits, offering a statistical mechanical explanation for black hole thermodynamics.

ABSTRACT

This review is based on lectures given at the 1992 Trieste Spring School on String Theory and Quantum Gravity and at the 1992 TASI Summer School in Boulder, Colorado.

Motivation & Objective

• To explore quantum gravity effects in black holes using string theory as a framework.
• To address the black hole information paradox through microscopic state counting.
• To derive the Bekenstein-Hawking entropy formula from quantum statistical mechanics in string theory.
• To examine extremal and near-extremal black holes as probes of quantum gravity.
• To clarify the role of duality and non-perturbative effects in black hole entropy.

Proposed method

• Utilizes string theory to model black holes as bound states of D-branes and other extended objects.
• Applies statistical mechanics to count microstates of extremal black holes using degeneracy of BPS states.
• Employs duality symmetries (e.g., S-duality) to relate strong-coupling black hole solutions to weak-coupling configurations.
• Analyzes the near-horizon geometry of extremal black holes to extract entropy from quantum degeneracy.
• Uses the attractor mechanism to fix moduli at the horizon, stabilizing entropy calculations.
• Applies the Cardy formula to compute entropy from the central charge of the dual CFT on the horizon.

Experimental results

Research questions

• RQ1 How can black hole entropy be derived from quantum statistical mechanics in string theory?
• RQ2 What is the microscopic origin of the Bekenstein-Hawking entropy formula?
• RQ3 How do duality symmetries relate different descriptions of the same black hole system?
• RQ4 Can the information paradox be resolved through exact counting of quantum microstates?
• RQ5 What role do extremal black holes play in probing quantum gravity effects?

Key findings

• The entropy of extremal black holes in string theory matches the Bekenstein-Hawking formula through exact counting of BPS microstates.
• The degeneracy of D-brane configurations reproduces the logarithmic corrections to black hole entropy.
• The attractor mechanism stabilizes moduli at the horizon, ensuring universal entropy independent of initial moduli values.
• Duality symmetries allow the computation of strong-coupling black hole properties via weak-coupling string theory.
• The near-horizon geometry of extremal black holes is described by an AdS2 × S² factor, supporting a dual CFT with finite central charge.
• The Cardy formula applied to the dual CFT reproduces the macroscopic entropy, confirming the statistical origin of black hole entropy.