Axisymmetric Solutions to Einstein Field Equations via Integral Transforms

TL;DR

This paper introduces new axisymmetric vacuum solutions to Einstein's equations using integral transforms, revealing naked singularities and emphasizing the significance of such solutions in general relativity.

Contribution

It presents novel axisymmetric solutions obtained via Hankel integral transforms, expanding the set of known solutions with naked singularities in Einstein's field equations.

Findings

All solutions exhibit naked singularities.

Solutions display features like blueshift and specific singularity geometries.

Comparison shows similarities with existing solutions with naked singularities.

Abstract

In this paper, we present new axisymmetric and reflection symmetric vacuum solutions to the Einstein field equations. They are obtained using the Hankel integral transform method and all three solutions exhibit naked singularities. Our results further reinforce the importance and special character of axisymmetric solutions in general relativity and highlight the role of integral transforms methods in solving complex problems in this field. We compare our results to already existing solutions which exhibit the same type of singularities. In this context we notice that most known axial-symmetric solutions possess naked singularities. A discussion of characteristic features of the newly found metrics, e.g., blueshift and the geometry of the singularities, is given.