Simulating the dynamics of relativistic stars via a light-cone approach

TL;DR

This paper introduces a novel light-cone based numerical framework for simulating relativistic stars, enabling accurate gravitational wave extraction and stable long-term evolution of neutron star models.

Contribution

The authors develop a new axisymmetric light-cone numerical scheme for Einstein-perfect fluid systems, improving gravitational wave extraction and stability in relativistic star simulations.

Findings

Successfully simulated pulsations of relativistic stars

Achieved energy conservation in perturbed neutron star models

Extracted gravitational wave signals consistent with quadrupole predictions

Abstract

We present new numerical algorithms for the coupled Einstein-perfect fluid system in axisymmetry. Our framework uses a foliation based on a family of light cones, emanating from a regular center, and terminating at future null infinity. This coordinate system is well adapted to the study of the dynamical spacetimes associated with isolated relativistic compact objects such as neutron stars. In particular, the approach allows the unambiguous extraction of gravitational waves at future null infinity and avoids spurious outer boundary reflections. The code can accurately maintain long-term stability of polytropic equilibrium models of relativistic stars. We demonstrate global energy conservation in a strongly perturbed neutron star spacetime, for which the total energy radiated away by gravitational waves corresponds to a significant fraction of the Bondi mass. As a first application we present results in the study of pulsations of axisymmetric relativistic stars, extracting the frequencies of the different fluid modes in fully relativistic evolutions of the Einstein-perfect fluid system and making a first comparison between the gravitational news function and the predicted wave using the approximations of the quadrupole formula.