# A family of scalar-Einstein and vacuum Brans-Dicke axisymmetric solutions

## TL;DR

This paper introduces a novel method linking static axially symmetric vacuum solutions in general relativity to a class of scalar-Einstein solutions with specific mass and angular momentum, revealing new Kerr-like solutions in Brans-Dicke theory.

## Contribution

It establishes a one-to-one correspondence between vacuum GR solutions and scalar-Einstein solutions, and constructs new stationary axially symmetric solutions in Brans-Dicke theory.

## Key findings

- A new method for solution correspondence is proposed.
- A specific asymptotically flat solution with a ringlike naked singularity is analyzed.
- The solution reduces to Kerr when scalar charge vanishes but not to Fisher-Janis-Newman-Winicour for zero rotation.

## Abstract

A new method is proposed, that establishes a one to one correspondance between the whole set of static axially symmetric vacuum GR solutions and a specific class of stationary axially symmetric scalar-Einstein solutions having a given mass and a given angular momentum. The method explicitly takes advantage of the Kerr metric Ricci flatness. This also results in a class of stationary axially symmetric vacuum, ie Kerrlike, Brans-Dicke solutions. A particular solution, that is asymptotically flat, is more closely considered. It converges to Kerr for a vanishing scalar charge, but fails to converge to the Fisher-Janis-Newman-Winicour solution for a vanishing "rotation parameter". This solution exhibits a naked singularity having a ringlike structure.