Bondian frames to couple matter with radiation

TL;DR

This paper develops a numerical relativity scheme using Bondian frames to study the nonlinear evolution of matter coupled with a massless scalar field, demonstrating its effectiveness through various models and boundary conditions.

Contribution

It introduces a novel characteristic formulation with Bondian frames for coupled matter and scalar fields, ensuring proper boundary matching and physical interpretation.

Findings

Successful evolution of scalar waves on different backgrounds

Conservation of energy and Newman-Penrose constant observed

Boundary conditions and matching conditions are effectively implemented

Abstract

A study is presented for the non linear evolution of a self gravitating distribution of matter coupled to a massless scalar field. The characteristic formulation for numerical relativity is used to follow the evolution by a sequence of light cones open to the future. Bondian frames are used to endow physical meaning to the matter variables and to the massless scalar field. Asymptotic approaches to the origin and to infinity are achieved; at the boundary surface interior and exterior solutions are matched guaranteeing the Darmois--Lichnerowicz conditions. To show how the scheme works some numerical models are discussed. We exemplify evolving scalar waves on the following fixed backgrounds: A) an atmosphere between the boundary surface of an incompressible mixtured fluid and infinity; B) a polytropic distribution matched to a Schwarzschild exterior; C) a Schwarzschild- Schwarzschild spacetime. The conservation of energy, the Newman--Penrose constant preservation and other expected features are observed.