2019/07/01 by Kadri İlker Berktav, Berktav, Kadri İlker
Physics and Astronomy · #14A20 #14A30 #14D23 #18F20 #70S15 #81T35 #83C99 #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1907.00665
openalex publication_date 2019/07/01 · openalex created_date 2023/01/27 · openalex updated_date 2026/07/28
In this paper, we examine stacky structures in Einstein's theory of gravity. In brief, we first give a construction of the moduli stack of solutions to (vacuum) Einstein field equations on n-dimensional spacetimes, with vanishing cosmological constant. Using a similar approach, we also study Einstein's gravity on families of manifolds and define another stack encoding this situation as well. Secondly, we focus on the gauge theoretical interpretation of 3D gravity and the concept of equivalence of 3D quantum gravity with gauge theory. By equivalence, we essentially mean the existence of an isomorphism between the phase spaces of 3D gravity and the associated gauge theory. In this regard, we show that once it exists, the equivalence induces an isomorphism between the corresponding moduli stacks.