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Spectral Metric and Einstein Functionals (2206.02587v2)
Published 3 Jun 2022 in math.DG, gr-qc, math-ph, math.MP, math.OA, and math.QA
Abstract: We define bilinear functionals of vector fields and differential forms, the densities of which yield the metric and Einstein tensors on even-dimensional Riemannian manifolds. We generalise these concepts in non-commutative geometry and, in particular, we prove that for the conformally rescaled geometry of the noncommutative two-torus the Einstein functional vanishes.
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