Dark Spring - a Simple Interpretation of the Susskind- Horowitz-Polchinsky Correspondence between Schwarzschild Black Hole and Strings

TL;DR

This paper offers a simplified classical and phenomenological interpretation of the Susskind-Horowitz-Polchinski correspondence, linking black hole thermodynamics to a model of a dark spring with quantized properties.

Contribution

It introduces a classical mechanical model called dark spring, providing a straightforward derivation of black hole thermodynamics and a novel analogy to string theory correspondence.

Findings

Dark spring characteristics match black hole entropy and temperature.

A simple algebraic relation links dark spring parameters to string coupling and excitation level.

The model offers an intuitive classical analogy to complex string-black hole duality.

Abstract

In this work we suggest a simplified interpretation of Susskind-Horowitz-Polchinski correspondence between Schwarzschild black hole and strings. Firstly, similarly to naive, classical mechanical Laplace determination of the Schwarzschild radius, we suggest a simple, classical mechanical equation. It determines amplitude of such sufficiently strong classical elastic force that forbids escape of a Planck mass particle moving by speed of light from end of corresponding classical elastic spring, simply called dark spring. Also, by use of a formal identity between given elastic force and Schwarzschild gravitational "force", we introduce phenomenologically a simple quantization rule. It states that circumference (corresponding to elastic force amplitude equivalent formally to Schwarzschild radius) holds natural number of corresponding reduced Compton's wave length. (It is deeply analogous to Bohr's quantization postulate in Bohr's atomic theory interpreted by de Broglie relation.) Then, very simply (by simple algebraic equations only) and surprisingly, we obtain such dark spring characteristics corresponding to basic thermodynamical characteristics (Bekenstein-Hawking entropy and Hawking temperature) for corresponding Schwarzschild black hole. Finally, simple comparison between obtained dark spring characteristics and Susskind-Horowitz-Polchinski correspondence, a simple correspondence between strings and dark spring, i.e. classical linear harmonic oscillator follows. Square root of the elasticity coefficient of the dark spring corresponds to quotient of one string coupling g and Newtonian gravitational constant, or, classical elasticity coefficient of the dark spring corresponds to reciprocal (inverse) value of the square root of a string state excitation level N.