Noncommutative Heisenberg algebra in the neighbourhood of a generic null surface

2018/02/28 by Krishnakanta Bhattacharya, Bibhas Ranjan Majhi
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Gravitation #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Null (SQL) #Physics #Pure mathematics #Quantum mechanics #Spacetime #gr-qc #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2018.07.025

published as Nuclear Physics B 934 (2018) 557 · Modified version with several added comments, To appear in Nucl. Phys. B

openalex created_date 2018/02/23 · arxiv created 2018/07/26 · openalex publication_date 2018/07/31 · arxiv updated 2018/08/07 · openalex updated_date 2026/08/05

Abstract

We show that the diffeomorphisms, which preserve the null nature for a generic null metric very near to the null surface, provide noncommutative Heisenberg algebra. This is the generalization of the earlier work Majhi (2017) [21] , done for the Rindler horizon. The present analysis revels that the algebra is very general as it is obtained for a generic null surface and is applicable for any spacetime horizon. Finally using these results, the entropy of the null surface is derived in the form of the Cardy formula. Our analysis is completely off-shell as no equation of motion is used. We believe present discussion can illuminate the paradigm of “gravity as an emergent phenomenon” and could be a candidate to probe the origin of gravitational entropy.

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