2014/12/17 by Michael Reiterer, Reiterer, Michael, Eugene Trubowitz +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #gr-qc #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1412.5561
41 pages
arxiv created 2014/12/17 · openalex publication_date 2014/12/17 · arxiv updated 2014/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a graded Lie algebra in which a solution to the vacuum Einstein equations is any element of degree 1 whose bracket with itself is zero. Each solution generates a cochain complex, whose first cohomology is linearized gravity about that solution. We gauge-fix to get a smaller cochain complex with the same cohomologies (deformation retraction). The new complex is much smaller, it consists of the solution spaces of linear homogeneous wave equations (symmetric hyperbolic equations). The algorithm that produces these gauges and wave equations is both for linearized gravity and the full Einstein equations. The gauge groupoid is the groupoid of rank 2 complex vector bundles.