Size scaling of self gravitating polymers and strings

TL;DR

This paper investigates how self-gravitating polymers behave, revealing a balance point where attractive and repulsive forces determine their size, which can approach black hole scales, with implications for understanding gravitating strings.

Contribution

It introduces a mean field model of self-gravitating polymers incorporating Newtonian and contact interactions, analyzing size scaling and phase diagrams across dimensions.

Findings

Existence of a scaling region balancing forces.

Repulsive interactions increase critical gravitational coupling.

Polymer size can reach Schwarzschild radius, resembling black holes.

Abstract

We study a statistical ensemble of a single polymer with self gravitational interaction. This is a model of a gravitating string --- the precursor of a black hole. We analyze averaged sizes by mean field approximations with an effective Hamiltonian a la Edwards with Newtonian potential as well as a contact repulsive interaction. We find that there exists a certain scaling region where the attractive and the repulsive forces balance out. The repulsive interaction pushes the critical gravitational coupling to a larger value, at which the size of a polymer becomes comparable to its Schwarzschild radius, and as a result the size of the corresponding black hole increases considerably. We show phase diagrams in various dimensions that clarify how the size changes as the strengths of repulsive and gravitational forces vary.