Spacetime Geometry as Statistic Ensemble of Strings

Marcelo Botta Cantcheff

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arXiv · 1105.3658

Spacetime Geometry as Statistic Ensemble of Strings

Marcelo Botta Cantcheff

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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.

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Marcelo Botta Cantcheff. 2011-05-18. Spacetime Geometry as Statistic Ensemble of Strings. https://arxiv.org/abs/1105.3658

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