Gravitational singularities, scattering maps for bouncing, and structure-preserving algorithms

TL;DR

This paper explores the role of multi-scale wave structures and junction conditions in physics, focusing on gravitational singularities, bouncing cosmologies, and the development of structure-preserving algorithms for fluid flow simulations.

Contribution

It reviews the recent concept of singularity scattering maps for defining bouncing spacetimes and presents new numerical algorithms for simulating small-scale fluid phenomena in cosmological geometries.

Findings

Introduction of singularity scattering maps for bouncing spacetimes

Development of structure-preserving algorithms for fluid flow simulations

Numerical results demonstrating small-scale phenomena in cosmological models

Abstract

This note emphasizes the role of multi-scale wave structures and junction conditions in many fields of physics, from the dynamics of fluids with non-convex equations of state to the study of gravitational singularities and bouncing cosmologies in general relativity. Concerning the definition and construction of bouncing spacetimes, we review the recent proposal in collaboration with B. Le Floch and G. Veneziano based on the notion of singularity scattering maps. We also present recent numerical investigations of small-scale phenomena arising in compressible fluid flows on FRLW or Kasner geometries for which we developed structure-preserving algorithms.