# A Note on the Possible Existence of an Instanton-like Self-Dual Solution to Lattice Euclidean Gravity

## TL;DR

This paper constructs a self-dual solution in lattice Euclidean gravity that is globally Euclidean at infinity, differing from the continuous Eguchi-Hanson solution, and explores its properties.

## Contribution

It introduces a novel lattice Euclidean gravity solution that is asymptotically globally Euclidean, expanding understanding of discrete gravitational models.

## Key findings

- Lattice self-dual solution constructed
- Solution is asymptotically globally Euclidean
- Differs from continuous Eguchi-Hanson solution

## Abstract

The self-dual solution to lattice Euclidean gravity is constructed. In contrast to the well known Eguchi-Hanson solution to continuous Euclidean Gravity, the lattice solution is asymptotically {\it{globally}} Euclidean, i.e., the boundary of the space as $r\longrightarrow\infty$ is $S^3=SU(2)$.