String Thermalization in Static Spacetimes

TL;DR

This paper investigates how string states evolve and thermalize in a static spacetime with a horizon and naked singularity, revealing a factorization of their phase space distribution into thermal components.

Contribution

It introduces a novel analysis of string thermalization in a complex spacetime, linking the Fokker-Planck solution to thermal distributions under uncertainty principle constraints.

Findings

String phase space distribution factorizes into thermal components.

Thermalization process characterized by a diffusion approach near the horizon.

Uncertainty principle constrains the classical variables involved.

Abstract

We study the evolution, the transverse spreading and the subsequent thermalization of string states in the Weyl static axisymmetric spacetime. This possesses a singular event horizon on the symmetry axis and a naked singularity along the other directions. The branching diffusion process of string bits approaching the singular event horizon provides the notion of temperature that is calculated for this process. We find that the solution of the Fokker-Planck equation in the phase space of the transverse variables of the string, can be factored as a product of two thermal distributions, provided that the classical conjugate variables satisfy the uncertainty principle. We comment on the possible physical significance of this result.