Hydrodynamical Misner-Sharp Formulation for Gravitational Collapse in Scalar-Tensor Theories

Abstract

We study the problem of gravitational collapse in the context of scalar-tensor theories of Gravity. We introduce a new hydrodynamical formulation in the Einstein frame, inspired by that of Misner and Sharp. We obtain the equilibrium Tolman-Oppenheimer-Volkoff condition that we use to find valid initial states of the problem within this framework. For illustration purposes, we present the minimal version of the initial phases of the collapse together with an analysis of the corresponding junction conditions.

Figures (2)

• Figure 1: Evolution in time of the matter energy density (black) and the scalar field energy density (blue) for an idealized homogeneous stellar collapse choosing $\alpha=0.2$.
• Figure 2: Evolution of the scale factor $f$ in a homogeneous stellar collapse for different values of the coupling constant $\alpha$. The line at the top corresponds to $\alpha=0$ (blue), the middle one to $\alpha=0.2$ (orange), and the one in the bottom to $\alpha=0.4$ (green).