# Noncomutativity in near horizon symmetries in gravity

## TL;DR

This paper reveals that near horizon symmetry generators in gravity form a noncommutative Heisenberg algebra, suggesting a quantum structure of horizons and providing insights into the microscopic origin of entropy.

## Contribution

It demonstrates noncommutativity in near horizon symmetries across all null surfaces and dimensions, linking algebraic structures to horizon entropy via the Cardy formula.

## Key findings

- Near horizon symmetry generators satisfy noncommutative Heisenberg algebra.
- Central charge identified using Sugawara construction.
- Horizon entropy matches the Cardy formula.

## Abstract

We have a new observation that near horizon symmetry generators, corresponding to diffeomorphisms which leave the horizon structure invariant, satisfy noncommutative Heisenberg algebra. The results are valid for any null surfaces (which has Rindler structure in the near null surface limit) and in any spacetime dimensions. Using Sugawara construction technique the central charge is identified. It is shown that the horizon entropy is consistent with the standard form of Cardy formula. Therefore we feel that the noncommutative algebra might leads to quantum mechanics of horizon and also can probe into the microscopic description of entropy.