On Stationary Axially Symmetric Solutions in Brans-Dicke Theory

TL;DR

This paper reexamines stationary, axially symmetric solutions in Brans-Dicke theory, introduces a new solution-generating technique, and constructs several known and novel solutions, including a generalization of the Kerr-Newman solution.

Contribution

It develops a two-parameter extension of solution-generating methods in Brans-Dicke theory and constructs new axially symmetric solutions, including a generalized Kerr-Newman type solution.

Findings

Derived Ernst equations for axially symmetric electrovacuum in BD theory.

Constructed a general BD-Maxwell solution of Plebanski-Demianski type.

Analyzed physical properties and test particle motion in a Kerr-Newman-NUT--type solution.

Abstract

Stationary, axially symmetric Brans-Dicke-Maxwell solutions are reexamined in the framework of the Brans-Dicke (BD) theory. We see that, employing a particular parametrization of the standard axially symmetric metric simplifies the procedure of obtaining the Ernst equations for axially symmetric electrovacuum space-times for this theory. This analysis also permits us to construct a two parameter extension in both Jordan and Einstein frames of an old solution generating technique frequently used to construct axially symmetric solutions for BD theory from a seed solution of general relativity. As applications of this technique, several known and new solutions are constructed including a general axially symmetric BD-Maxwell solution of Plebanski-Demianski with vanishing cosmological constant, i.e. the Kinnersley solution and general magnetized Kerr-Newman--type solutions. Some physical properties and the circular motion of test particles for a particular subclass of Kinnersley solution, i.e., a Kerr-Newman-NUT--type solution for BD theory, are also investigated in some detail.