A Note on the Near Horizon Charges for the Five Dimensional Myers-Perry Black Holes

TL;DR

This paper investigates the near horizon charges of five-dimensional Myers-Perry black holes with equal rotation parameters, revealing a Heisenberg algebra structure in the near horizon symmetry algebra.

Contribution

It extends the analysis of near horizon symmetries to five-dimensional black holes and identifies a novel algebraic structure in their near horizon charges.

Findings

Near horizon charges are computed for five-dimensional Myers-Perry black holes.

The near horizon algebra is shown to be an infinite set of Heisenberg algebras.

The gauge flatness condition is violated due to non-vanishing field strength.

Abstract

Inspired by the recent work on the spacetime structure near generic black hole horizons [1], the near horizon charges for an explicit example in higher dimensions than four (d > 4), namely for the five dimensional Myers-Perry metric with two equal rotation parameter are found in Hamiltonian formalism. Finding the supertranslation and the one-form superrotation, it is proved that the Myers-Perry black hole with two equal rotation parameter a = b does not satisfy the gauge flatness condition due to the non-vanishing associated field strength in five dimensional spacetime. It is shown that as the near horizon limit of such a metric satisfies a specific set of boundary conditions, the near horizon algebra can be represented as an infinitely many copies of Heisenberg algebras as a generalisation to the Kerr case in four dimensions.