Scattering laws for interfaces in self-gravitating matter flows

TL;DR

This paper develops a framework for analyzing the evolution of self-gravitating matter with phase transitions, introducing scattering maps on hypersurfaces to ensure a complete and consistent macroscopic description within Einstein-Euler systems.

Contribution

It introduces a novel approach using scattering relations on hypersurfaces to model interfaces in self-gravitating matter flows, ensuring uniqueness and physical consistency.

Findings

Formulated local evolution problem for Einstein-Euler system with interfaces.

Derived universal relations and model-dependent parameters for scattering maps.

Ensured compatibility with Einstein and Euler equations, including constraint propagation.

Abstract

We consider the evolution of self-gravitating matter fields that may undergo phase transitions, and we connect ideas from phase transition dynamics with concepts from bouncing cosmology. Our framework introduces scattering maps prescribed on two classes of hypersurfaces: a gravitational singularity hypersurface and a fluid-discontinuity hypersurface. By analyzing the causal structures induced by the light cone and the acoustic cone, we formulate a local evolution problem for the Einstein-Euler system in the presence of such interfaces. We explain how suitable scattering relations must supplement the field equations in order to ensure uniqueness and thus yield a complete macroscopic description of the evolution. This viewpoint builds on a theory developed in collaboration with G. Veneziano for quiescent (velocity-dominated) singularities in solutions of the Einstein equations coupled to a scalar field, where the passage across the singular hypersurface is encoded by a singularity scattering map. The guiding question is to identify junction prescriptions that are compatible with the Einstein and Euler equations, in particular with the propagation of constraints. The outcome is a rigid set of universal relations, together with a family of model-dependent parameters. Under physically motivated requirements (general covariance, causality, constraint compatibility, and ultra-locality), we aim to classify admissible scattering relations arising from microscopic physics and characterizing, at the macroscopic level, the dynamics of a fluid coupled to Einstein gravity.