Infinite Charge Algebra of Gravitational Instantons

TL;DR

This paper derives an infinite set of conserved charges for gravitational instantons with rotational symmetry using minitwistor formalism, revealing an infinite-dimensional algebra related to area-preserving diffeomorphisms.

Contribution

It introduces a novel approach to identify an infinite number of conserved charges for gravitational instantons via minitwistor formalism, establishing their algebraic structure.

Findings

Derived infinite conserved charges for gravitational instantons.

Established the algebra of charges as isomorphic to area-preserving diffeomorphisms.

Connected the algebra to a well-known infinite-dimensional symmetry group.

Abstract

Using a formalism of minitwistors, we derive infinitely many conserved charges for the $sl(\infty )$-Toda equation which accounts for gravitational instantons with a rotational Killing symmetry. These charges are shown to form an infinite dimensional algebra through the Poisson bracket which is isomorphic to two dimensional area preserving diffeomorphism with central extentions.