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

Understand

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.