Existence of naked singularities in Brans-Dicke theory of gravitation. An analytical and numerical study

TL;DR

This paper demonstrates the existence of naked singularities in Brans-Dicke gravity through analytical and numerical methods, extending previous work on Einstein-scalar fields by incorporating a dynamic coupling parameter.

Contribution

It introduces a new class of solutions in Brans-Dicke theory where a key parameter becomes dynamical, broadening the understanding of naked singularities in scalar-tensor gravitation.

Findings

Existence of spherically symmetric naked singularities in Brans-Dicke theory.

Analytical confirmation of properties similar to those found by Christodoulou.

Numerical analysis of the properties of these spacetimes.

Abstract

Within the framework of the scalar-tensor models of gravitation and by relying on analytical and numerical techniques, we establish the existence of a class of spherically symmetric spacetimes containing a naked singularity. Our result relies on and extends a work by Christodoulou on the existence of naked singularities for the Einstein-scalar field equations. We establish that a key parameter in Christodoulou's construction couples to the Brans-Dicke field and becomes a dynamical variable, which enlarges and modifies the phase space of solutions. We recover analytically many properties first identified by Christodoulou, in particular the loss of regularity (especially at the center), and then investigate numerically the properties of these spacetimes.