A noncommutative geometric approach to the quantum structure of spacetime

摘要: Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for spaces embedded in higher dimensions the last few years. The theory was applied to construct version of general relativity, which is expected capture some essential structural features spacetime at Planck scale. Examples spacetimes were investigated detail. These include quantisations plane-fronted gravitational waves, quantum Schwarzschild Schwarzschild-de Sitter spacetime, quantun Tolman relevant collapse. Here briefly review its application study structure spacetime.