Maximally Symmetric Spacetimes emerging from thermodynamic fluctuations

Instituto de Ciencias Nucleares,Universidad Nacional Auto´noma de M´exico,AP 70543, M´exico, DF 04510, Mexico.(Dated: April 3, 2015)In this work we prove that the maximally symmetric vacuum solutions of General Relativityemerge from the geometric structure of statistical mechanics and thermodynamic fluctuation the-ory. To present our argument, we begin by showing that the pseudo-Riemannian structure of theThermodynamic Phase Space is a solution to the vacuum Einstein-Gauss-Bonnet theory of gravitywith a cosmological constant. Then, we use the geometry of equilibrium thermodynamics to demon-strate that the maximally symmetric vacuum solutions of Einstein’s Field Equations – Minkowski,de-Sitter and Anti-de-Sitter spacetimes – correspond to thermodynamic fluctuations. Moreover, weargue that these might be the only possible solutions that can be derived in this manner. Thus, theresults presented here are the first concrete examples of spacetimes effectively emerging from thethermodynamic limit over an unspecified microscopic theory without any further assumptions.