2015/03/28 by Alessandro Bravetti, A. Bravetti, C. S. López-Monsalvo +6 · 5 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmological constant #Cosmology and Gravitation Theories #De Sitter universe #Einstein #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #General relativity #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematical physics #Minkowski space #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Statistical mechanics #Theoretical physics #Thermodynamic limit #Thermodynamics #Universe #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1503.08358
published in arXiv (Cornell University) (Cornell University) · Preliminary version. Comments are welcome! Corrected equation referencing
openalex publication_date 2015/03/28 · arxiv created 2015/03/31 · arxiv updated 2015/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we prove that the maximally symmetric vacuum solutions of General Relativity emerge from the geometric structure of statistical mechanics and thermodynamic fluctuation theory. To present our argument, we begin by showing that the pseudo-Riemannian structure of the Thermodynamic Phase Space is a solution to the vacuum Einstein-Gauss-Bonnet theory of gravity with a cosmological constant. Then, we use the geometry of equilibrium thermodynamics to demonstrate that the maximally symmetric vacuum solutions of Einstein's Field Equations -- Minkowski, de-Sitter and Anti-de-Sitter spacetimes -- correspond to thermodynamic fluctuations. Moreover, we argue that these might be the only possible solutions that can be derived in this manner. Thus, the results presented here are the first concrete examples of spacetimes effectively emerging from the thermodynamic limit over an unspecified microscopic theory without any further assumptions.