The Generic Sudden Singularity in Brans-Dicke Theory

TL;DR

This paper develops a formal asymptotic series solution for Brans-Dicke equations near a sudden singularity, revealing geodesic completeness and shock wave characteristics, and compares it with general relativity.

Contribution

It provides the first detailed asymptotic solution for Brans-Dicke theory near sudden singularities, including arbitrary functions and geodesic analysis.

Findings

Solution contains eleven arbitrary functions of spatial coordinates.

The solution is geodesically complete and resembles a shock wave.

The solution is weak in Tipler and Krolak senses, similar to GR.

Abstract

We construct a formal asymptotic series expansion for a general solution of the Brans-Dicke equations with a fluid source near a sudden singularity. This solution contains eleven independent arbitrary functions of the spatial coordinates as required by the Cauchy problem of the theory. We show that the solution is geodesically complete and has the character of a shock wave in the sudden asymptotic region. This solution is weak in the senses of Tipler and Krolak as in the corresponding case of general relativity.