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

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.

15 pages, 10 figures, submitted to Phys. Rev. D

References in corpus (5)

• Gravitational waves from relativistic rotational core collapse
• Axisymmetric Modes of Rotating Relativistic Stars in the Cowling Approximation
• Spherical collapse of supermassive stars: neutrino emission and gamma-ray bursts
• Scalar field induced oscillations of neutron stars and gravitational collapse
• Characteristic Evolution and Matching

Cited by in corpus (21)

• Rotating Stars in Relativity
• Rotating Stars in Relativity
• Characteristic Evolution and Matching
• Gravitational waves from axisymmetrically oscillating neutron stars in general relativistic simulations
• Collapse of Rotating Supramassive Neutron Stars to Black Holes: Fully General Relativistic Simulations
• Axisymmetric core collapse simulations using characteristic numerical relativity
• Characteristic Evolution and Matching
• Gravitational wave extraction based on Cauchy-characteristic extraction and characteristic evolution
• Spherical excision for moving black holes and summation by parts for axisymmetric systems
• Adaptive Mesh Refinement for Characteristic Codes
• Affine-null metric formulation of General Relativity at two intersecting null hypersurfaces
• Fully relativistic three-dimensional Cauchy-characteristic matching for physical degrees of freedom
• Gravitational waves in dynamical spacetimes with matter content in the Fully Constrained Formulation
• First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations
• Central equation of state in spherical characteristic evolutions
• Gauge structure of the Einstein field equations in Bondi-like coordinates
• Numerical convergence of model Cauchy-characteristic extraction and matching
• The Bondi-Sachs metric at the vertex of a null cone: axially symmetric vacuum solutions
• Simulations of gravitational collapse in null coordinates: I. Formulation and weak-field tests in generalised Bondi gauges
• Slowly rotating Kerr metric derived from the Einstein equations in affine-null coordinates
• Conformal compactification and affine-null metric formulation of the Einstein equations