Central equation of state in spherical characteristic evolutions

TL;DR

This paper investigates the evolution of a perfect-fluid sphere coupled with scalar radiation, revealing a central equation of state and conditions for regularity in a conformally flat spacetime, with implications for numerical relativity.

Contribution

It derives a central equation of state for a fluid coupled to scalar radiation in spherical symmetry, ensuring regularity at the center and informing numerical hydrodynamic models.

Findings

The fluid satisfies $ ho_c+3p_c=$ constant at the center.

The fluid is anisotropic and radiative due to the scalar field but becomes perfect and non radiative at the center.

Results aid in developing numerical relativistic hydrodynamic solvers.

Abstract

We study the evolution of a perfect--fluid sphere coupled to a scalar radiation field. By ensuring a Ricci invariant regularity as a conformally flat spacetime at the central world line we find that the fluid coupled to the scalar field satisfies the equation of state $\rho_c+3p_c=$ constant at the center of the sphere, where the energy $\rho_c$ density and the pressure $p_c$ do not necessarily contain the scalar field contribution. The fluid can be interpreted as anisotropic and radiant because of the scalar field, but it becomes perfect and non radiative at the center of the sphere. These results are being currently considered to build up a numerical relativistic hydrodynamic solver.