Spectral Metric and Einstein Functionals
Differential Geometry
2023-06-09 v2 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Operator Algebras
Quantum Algebra
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.
Cite
@article{arxiv.2206.02587,
title = {Spectral Metric and Einstein Functionals},
author = {Ludwik Dąbrowski and Andrzej Sitarz and Paweł Zalecki},
journal= {arXiv preprint arXiv:2206.02587},
year = {2023}
}
Comments
Final version, typos corrected