Spacetime Geometry as Statistic Ensemble of Strings

Abstract

Jacobson theorem (Ref. \cite{jacobson}) shows that Einstein gravity may be understood as a thermodynamical equation of state; a microscopic realization of this result is however lacking. In this paper, we propose that this may be achieved by assuming the spacetime geometry as a macroscopic system, whose thermodynamical behavior is described by a statistical ensemble, whose microscopic components are low-dimensional geometries. We show that this picture is consistent with string theory by proposing a particular model for the microscopic geometry, where the spacetime metric plays the role of an ordinary thermodynamical potential in a special ensemble. In this scenario, Einstein equation is indeed recovered as an equation of state, and the black hole thermodynamics is reproduced in a thermodynamic limit (large length scales). The model presented here is background-independent and, in particular, it provides an alternative formulation of string theory.