Analyzing the radial geodesics of the Campanelli-Lousto solutions

TL;DR

This paper investigates the properties of a family of Brans-Dicke vacuum solutions, focusing on singularity avoidance, metric signature changes, and radial geodesics, providing new insights into their geometric and physical characteristics.

Contribution

It offers a comprehensive analysis of a lesser-studied family of solutions, identifying non-singular cases and solving radial geodesics for specific scenarios.

Findings

Identified solutions that avoid singularities at metric divergence points

Analyzed metric signature changes across critical points

Derived radial geodesic solutions for particular cases

Abstract

When dealing with a spacetime, one usually searches for singularities, black holes, white holes and wormholes due to their importance to the motion of particles. There is a family of solution of the Brans-Dicke vacuum equations that has not been fully studied from this perspective. In this paper, I study some properties of this family and find the complete set of solutions that avoids singularity at the point where the metric diverges or degenerates. The possible changes in the metric signature when passing through this point is analyzed. In addition, I also study the radial geodesics and obtain the solutions of some particular cases.