Gravitational Collapse and Singularity Formation in Brans-Dicke Gravity

TL;DR

This paper studies scalar-field-driven gravitational collapse in Brans-Dicke gravity, showing it can produce globally visible singularities that challenge the Cosmic Censorship Conjecture.

Contribution

It provides a numerical analysis of collapse dynamics in Brans-Dicke theory, revealing conditions under which singularities are visible and analyzing their strength and causal structure.

Findings

Collapse leads to central curvature singularities.

Singularities can be globally visible to null infinity.

Collapse scenarios challenge the Cosmic Censorship Conjecture.

Abstract

We investigate gravitational collapse driven solely by a self-interacting Brans--Dicke (BD) scalar field in the absence of ordinary matter. In this framework, the spacetime dynamics are governed solely by the scalar field $\Phi$, endowed with a self-interaction potential $V(\Phi)$ and non-minimally coupled to the Ricci scalar through the Brans--Dicke action. We numerically solve for the evolution of $\Phi(t)$ and the corresponding potential $V(\Phi)$ in order to track the collapse dynamics leading to singularity formation. Our analysis demonstrates that, for the energy densities $\rho \approx 1/a$ and $\rho \approx -\ln a$, the collapse inevitably leads to the formation of a central curvature singularity while consistently satisfying the weak energy condition. We further examine the causal structure of the resulting singularity and find that future-directed null geodesics originating from the singularity can propagate to future null infinity, making the singularity globally visible. The strength of the singularity is also examined by extending Tipler's strong curvature condition to the Brans--Dicke field equations. Overall, our findings indicate that gravitational collapse in scalar--tensor gravity can give rise to scenarios that challenge the Cosmic Censorship Conjecture, while underscoring the potential observational relevance of singularities formed through BD scalar-field-driven collapse.