Self-Excited Gravitational Instantons

TL;DR

This paper introduces self-excited gravitational instantons, a new class of solutions in teleparallel gravity that relate torsion and excitation forms, resembling Yang-Mills instantons and characterized by topological charges.

Contribution

It proposes a novel class of gravitational instantons where torsion equals excitation forms, expanding the landscape of solutions in teleparallel gravity.

Findings

Self-excited instantons are analogous to BPST instantons in Yang-Mills theory.

The gravitational action reduces to a topological Nieh-Yan term.

Axial torsion acts as a topological current.

Abstract

We present a novel approach to constructing gravitational instantons based on the observation that the gravitational action of general relativity in its teleparallel formulation can be expressed as a product of the torsion and excitation forms. We introduce a new class of solutions where these two forms are equal, which we term the self-excited instantons, and advocate for their use over the self-dual instantons of Eguchi and Hanson. These new self-excited instantons exhibit striking similarities to BPST instantons in Yang-Mills theory, as their action reduces to a topological Nieh-Yan term, which allows us to identify the axial torsion as a topological current and show that the gravitational action is given by a topological charge.