Noncomutativity in near horizon symmetries in gravity

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.