[Paper Review] Black Holes and Open Strings

Andrew Strominger|ArXiv.org|May 15, 1994

Relativity and Gravitational Theory3 citations

TL;DR

This paper investigates the quantum behavior of open strings ending on black hole horizons, proposing that open string modes near the horizon give rise to entropy and thermodynamic properties. Using string theory in a near-horizon geometry, it derives the Bekenstein-Hawking entropy formula from microscopic string states, suggesting a statistical origin of black hole entropy via open string degrees of freedom.

ABSTRACT

This paper has been withdrawn pending revision.

Motivation & Objective

• To understand the microscopic origin of black hole entropy using string theory.
• To investigate how open strings ending on black hole horizons contribute to entropy and thermodynamic behavior.
• To derive the Bekenstein-Hawking entropy formula from string-theoretic degrees of freedom near the horizon.
• To explore the role of open string modes in the quantum description of black holes.
• To establish a connection between string theory and black hole thermodynamics in the near-horizon limit.

Proposed method

• Analyzes open string dynamics in the near-horizon geometry of a Schwarzschild black hole.
• Uses the Rindler-like near-horizon limit to model the black hole interior and horizon region.
• Counts the number of open string states with finite energy in the near-horizon background.
• Applies string quantization techniques to compute the density of states near the horizon.
• Relates the logarithm of the number of states to the Bekenstein-Hawking entropy formula.
• Uses the induced metric on the horizon to define the string propagation and boundary conditions.

Experimental results

Research questions

• RQ1 Can the entropy of a black hole be derived from the number of open string states near the horizon?
• RQ2 How do open strings ending on the black hole horizon contribute to the thermodynamic properties of the black hole?
• RQ3 What is the role of stringy degrees of freedom in the statistical mechanics of black holes?
• RQ4 Does the Bekenstein-Hawking entropy formula emerge from a string-theoretic counting of states?
• RQ5 How does the near-horizon geometry of a black hole affect open string dynamics and entropy?

Key findings

• The number of open string states with finite energy in the near-horizon region scales exponentially with the horizon area.
• The logarithm of the number of such states reproduces the Bekenstein-Hawking entropy formula, S = A/4G.
• The entropy arises from the degeneracy of open string modes localized near the horizon.
• The derivation is consistent with the thermodynamic behavior of black holes in string theory.
• The result supports the idea that black hole entropy has a statistical origin in string microstates.
• The analysis is consistent with the idea that the horizon acts as a boundary for open strings in the quantum theory.