Extending Sibgatullin's ansatz for the Ernst potential to generate a richer family of axially symmetric solutions of Einstein's equations

TL;DR

This paper explores an extended ansatz for the Ernst potential to generate more diverse axially symmetric solutions of Einstein's equations, focusing on calculating multipole moments and describing spacetime around rotating compact objects.

Contribution

It introduces a mixed ansatz for the Ernst potential that includes additional parameters, enhancing the ability to model complex spacetime geometries.

Findings

Derived a method to compute multipole moments from the Ernst potential on the symmetry axis.

Proposed an extended ansatz for the Ernst potential with extra parameters.

Discussed the implications of ansatz choice on solution properties.

Abstract

The scope of this talk is to present some preliminary results on an effort, currently in progress, to generate an exact solution of Einstein's equation, suitable for describing spacetime around a rotating compact object. Specifically, the form of the Ernst potential on the symmetry axis and its connection with the multipole moments is discussed thoroughly. The way to calculate the multipole moments of spacetime directly from the value of the Ernst potential on the symmetry axis is presented. Finally, a mixed ansatz is formed for the Ernst potential including parameters additional to the ones dictated by Sibgatullin. Thus, we believe that this talk can also serve as a comment on choosing the appropriate ansatz for the Ernst potential.