Spacetime Singularities in Generalized Brans-Dicke Theories

TL;DR

This paper investigates classical singularity formation in generalized Brans-Dicke theories, showing that such singularities are unavoidable in collapsing objects but not in expanding cosmological models, which tend to resemble General Relativity.

Contribution

It proves that arbitrary coupling functions in generalized Brans-Dicke theories cannot prevent singularities in gravitational collapse, while cosmological solutions avoid Big Rip singularities and approach General Relativity.

Findings

Collapsing objects form singularities regardless of coupling function.

Expanding cosmologies are free of Big Rip singularities.

Cosmological solutions asymptotically approach General Relativity.

Abstract

We study the formation of classical singularities in Generalized Brans-Dicke theories that are natural extensions to Brans-Dicke where the kinetic term is modified by a new coupling function $\omega(\varphi)$. We discuss the asymptotic limit $\omega(\varphi)\rightarrow\infty$ and show that the system generically does not approach General Relativity. Given the arbitrariness of $\omega(\varphi)$, one can search for coupling functions chosen specifically to avoid classical singularities. However, we prove that this is not the case. Homogeneous and spherically symmetric collapsing objects form singularities for arbitrary coupling functions. On the other hand, expanding cosmological scenarios are completely free of Big Rip type singularities. In an expanding universe, the scalar field behaves at most as stiff matter, which makes these cosmological solutions asymptotically approach General Relativity.