Hydrodynamical Misner–Sharp formulation for gravitational collapse in scalar-tensor theories

Abstract

We study the dynamics of gravitational collapse within the framework of scalar-tensor theories of gravity. By adopting the Einstein frame, we develop a novel hydrodynamical formulation inspired by the Misner-Sharp approach, which allows for a self-consistent description of the interaction between the fluid and the scalar field. We derive the generalized Tolman–Oppenheimer–Volkoff (TOV) equation for hydrostatic equilibrium, identifying how the scalar field modifies the balance between pressure gradients and gravitational attraction through an effective mass, pressure and a non-minimal coupling term. This equilibrium condition is subsequently used to construct consistent initial configurations for the collapse process. To illustrate the dynamics, we analyze the initial phases of the contraction and the junction conditions required to match the interior hydrodynamical solution with a suitable exterior vacuum within this limit. Our results show that the scalar field introduces a dynamical feedback that accelerates the collapse compared to General Relativity. This formulation provides a robust theoretical framework for studying strong-field phenomena and potential black hole formation in alternative gravity theories.