
We show that the diffeomorphisms, which preserve the null nature for a generic null metric very near to the null surface, provide {\it noncommutative} Heisenberg algebra. This is the generalization of the earlier work (Phys. Rev. D95, 044020 (2017)) \cite{Majhi:2017fua}, 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 {\it 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.
Modified version with several added comments, To appear in Nucl. Phys. B
spacetime horizons, High Energy Physics - Theory, High Energy Physics - Theory (hep-th), Nuclear and particle physics. Atomic energy. Radioactivity, FOS: Physical sciences, PDEs on Heisenberg groups, Lie groups, Carnot groups, etc., QC770-798, Einstein's equations (general structure, canonical formalism, Cauchy problems), General Relativity and Quantum Cosmology (gr-qc), General Relativity and Quantum Cosmology, Relativistic cosmology
spacetime horizons, High Energy Physics - Theory, High Energy Physics - Theory (hep-th), Nuclear and particle physics. Atomic energy. Radioactivity, FOS: Physical sciences, PDEs on Heisenberg groups, Lie groups, Carnot groups, etc., QC770-798, Einstein's equations (general structure, canonical formalism, Cauchy problems), General Relativity and Quantum Cosmology (gr-qc), General Relativity and Quantum Cosmology, Relativistic cosmology
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