A proposal for quantum gravity and quantum mechanics of black hole

Abstract

We propose a quantum mechanical theory of quantum spaces described by large $N$ noncommutative geometry as a model for quantum gravity. The theory admits fuzzy sphere and fuzzy ellipsoid as solution. We show that these solutions reproduces precisely the horizon radius of a Schwarzschild black hole and a Kerr black hole.

Moreover our quantum mechanical description gives rise to a set of microstates over these geometries, which reproduces precisely the Bekenstein-Hawking entropy of black hole. These results provide strong support that our proposed theory of quantum spaces is a plausible candidate for the theory of quantum gravity.

The seminar is based on the following papers: 2406.01466, 2406.12704, plus recent unpublished results.

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