Size Scaling of Self Gravitating Polymers and Strings

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 a Newtonian potential as well as a contact repulsive interaction. We find that there exists a certain scaling region where the attractive and 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 the repulsive and gravitational forces vary.