On conical asymptotically flat manifolds

TL;DR

This paper proves a conjecture about the non-existence of certain asymptotically flat 4-manifolds and discusses recent progress in gravitational instantons, motivated by geometric and physical considerations.

Contribution

It establishes the non-existence of asymptotically flat 4-manifolds asymptotic to the half plane, resolving a conjecture by Petrunin and Tuschmann.

Findings

Proof of the conjecture on non-existence of specific 4-manifolds

Survey of recent developments in gravitational instantons

Discussion of open questions in the field

Abstract

We prove a conjecture of Petrunin and Tuschmann on the non-existence of asymptotically flat 4-manifolds asymptotic to the half plane. We also survey recent progress and questions concerning gravitational instantons, which serve as our motivation for studying this question.