Bondian frames to couple matter with radiation

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.

Nonadiabatic charged spherical evolution in the postquasistatic approximation

“…This investigation is an essential part of a long-term project which tries to incorporate the Müller-Israel-Stewart theory for dissipation and deviations from spherical symmetry, specially when considering electrically charged distributions. Besides being interesting in their own right, we believe that spherically symmetric fluid models are useful as a test bed for more general solvers in numerical relativity [27,28]. A general three-dimensional code must also be able to reproduce situations closer to equilibrium.…”

“…If the configuration is leaving equilibrium, the PQSA description seems to be enough and can be used as a test bed in numerical relativity [26]. Its systematic use of local Minkowskian and comoving observers, named Bondians, was used to reveal a central equation of state in adiabatic scenarios [27], and to couple matter with radiation [28].…”

Characteristic Evolution and Matching

“…It is interesting that the pressure vanishes in the final equilibrium state so that hydrostatic support is completely supplied by Coulomb repulsion. In subsequent work [24, 25], they applied their characteristic code to the evolution of a polytropic fluid sphere coupled to a scalar radiation field to study the central equation of state, conservation of the Newman-Penrose constant, the scattering of the scalar radiation off the polytrope and its late time decay. The work illustrates how characteristic evolution can be used to simulate radiation from a matter source in the simple context of spherical symmetry.…”

An evolution of adiabatic matter: a case for the quasistatic regime

“…Usually the scalar field is considered as a matter source [9]. The massless scalar field can be interpreted as an anisotropic fluid [10], but this is purely formal. At last the massless scalar field behaves as radiation does.…”