Axially Symmetric Exponential Metric

TL;DR

This paper introduces a new two-parameter family of axially symmetric solutions in general relativity that generalize the Yilmaz Exponential Metric, connecting it to the Curzon-Chazy spacetime and describing a traversable wormhole.

Contribution

It constructs a novel axially symmetric exponential metric within general relativity, extending the Yilmaz metric to include axial symmetry and interpolating between known solutions.

Findings

Introduces a two-parameter family of axially symmetric metrics.

Shows the metric describes a traversable wormhole.

Connects Yilmaz and Curzon-Chazy geometries.

Abstract

We revisit the Yilmaz Exponential Metric (YEM), which was recently shown to describe a traversable wormhole, and construct an axially symmetric generalization strictly within the framework of general relativity. Starting from a deformed spherically symmetric ansatz, we introduce a two-parameter family of Axially Symmetric Exponential Metric (ASEM) solutions that smoothly interpolate between the YEM and the Curzon-Chazy spacetime geometry.