A Quasiperiodic Gibbons--Hawking Metric and Spacetime Foam

TL;DR

This paper constructs a new quasiperiodic self-dual Gibbons--Hawking metric with multiple gravitational instantons per spacetime cell, using advanced mathematical functions, contributing to the understanding of spacetime foam as defined by Hawking.

Contribution

It introduces a novel quasiperiodic Gibbons--Hawking metric based on Weierstrass functions, expanding the class of known solutions related to spacetime foam.

Findings

New quasiperiodic self-dual metric constructed

Multiple gravitational instantons per spacetime cell achieved

Utilizes adapted Weierstrassian functions for solution

Abstract

We present a quasiperiodic self-dual metric of the Gibbons--Hawking type with one gravitational instanton per spacetime cell. The solution, based on an adaptation of Weierstrassian $\zeta$ and $\sigma$ functions to three dimensions, conforms to a definition of spacetime foam given by Hawking.