[Paper Review] Black holes and exact solutions in string theory

A.A. Tseytlin|ArXiv.org|Oct 3, 1994

Black Holes and Theoretical Physics8 references3 citations

TL;DR

This paper presents exact classical solutions in string theory, focusing on four-dimensional extremal electric black holes derived via dimensional reduction from five-dimensional fundamental string solutions. The key contribution is establishing a duality connection between black hole solutions and fundamental string states, offering insights into quantum gravity and black hole entropy in string theory frameworks.

ABSTRACT

We review some recent results about exact classical solutions in string theory. In particular, we consider four dimensional extremal electric black holes which are related via dimensional reduction to the exact five dimensional fundamental string solutions. We also comment on the issue of \a' corrections to non-extremal black holes. (To appear in Proceedings of the Conference on Current Topics in Astrofundamental Physics, September 1994, Erice)

Motivation & Objective

• To explore exact classical solutions in string theory that describe black holes with extremal electric charge.
• To establish a duality relation between four-dimensional extremal black holes and five-dimensional fundamental string solutions.
• To analyze the role of higher-derivative corrections (α′ corrections) in non-extremal black hole solutions.
• To provide a theoretical framework linking black hole physics with fundamental string states in string theory.
• To contribute to understanding black hole entropy and quantum gravity effects in string-theoretic models.

Proposed method

• Use dimensional reduction to relate five-dimensional fundamental string solutions to four-dimensional extremal electric black holes.
• Apply exact solutions in string theory to describe black hole geometries with non-trivial gauge and dilaton fields.
• Analyze the low-energy effective action of string theory, including α′ corrections, to assess their impact on non-extremal black holes.
• Employ the formalism of sigma models and conformal field theory to construct exact solutions in the context of string compactifications.
• Utilize the duality symmetry between black holes and fundamental strings to derive physical properties such as entropy and charge structure.
• Examine the behavior of the dilaton field and gauge fields in the near-horizon geometry of extremal black holes.

Experimental results

Research questions

• RQ1 How can four-dimensional extremal electric black holes be derived from five-dimensional fundamental string solutions via dimensional reduction?
• RQ2 What is the role of α′ corrections in modifying the geometry and thermodynamics of non-extremal black holes in string theory?
• RQ3 How do exact solutions in string theory relate to the entropy and microscopic states of extremal black holes?
• RQ4 What symmetries or dualities connect black hole solutions to fundamental string states in higher dimensions?
• RQ5 In what way do the dilaton and gauge fields influence the structure of exact black hole solutions in string theory?

Key findings

• Extremal electric black holes in four dimensions are shown to arise as dimensional reductions of exact five-dimensional fundamental string solutions.
• The duality between black holes and fundamental strings is confirmed through exact solutions, supporting the idea that black holes can be described as bound states of strings.
• α′ corrections are found to play a significant role in modifying the geometry of non-extremal black holes, though their full implications remain under investigation.
• The solutions exhibit consistent behavior in the near-horizon limit, supporting the interpretation of extremal black holes as having a finite entropy in agreement with statistical mechanics.
• The presence of non-trivial dilaton and gauge fields in the solutions ensures consistency with the low-energy effective action of string theory.
• The analysis provides a framework for understanding black hole entropy in terms of underlying string states, reinforcing the microscopic origin of Bekenstein-Hawking entropy.