Axisymmetric Solutions to Einstein Field Equations via Integral Transforms

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.