Numerical Relativity in Spherical Polar Coordinates: Off-center Simulations
arXiv:1501.05259 · doi:10.1103/PhysRevD.91.064035
Abstract
We have recently presented a new approach for numerical relativity simulations in spherical polar coordinates, both for vacuum and for relativistic hydrodynamics. Our approach is based on a reference-metric formulation of the BSSN equations, a factoring of all tensor components, as well as a partially implicit Runge-Kutta method, and does not rely on a regularization of the equations, nor does it make any assumptions about the symmetry across the origin. In order to demonstrate this feature we present here several off-centered simulations, including simulations of single black holes and neutron stars whose center is placed away from the origin of the coordinate system, as well as the asymmetric head-on collision of two black holes. We also revisit our implementation of relativistic hydrodynamics and demonstrate that a reference-metric formulation of hydrodynamics together with a factoring of all tensor components avoids problems related to the coordinate singularities at the origin and on the axes. As a particularly demanding test we present results for a shock wave propagating through the origin of the spherical polar coordinate system.
arXiv comment13 pages, 11 figures; matches version published in PRD
References in corpus (24)
- Evolution of Binary Black Hole Spacetimes
- Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
- Gravitational wave extraction from an inspiraling configuration of merging black holes
- On the Numerical Integration of Einstein's Field Equations
- Gauge conditions for long-term numerical black hole evolutions without excision
- Large Merger Recoils and Spin Flips From Generic Black-Hole Binaries
- New Formalism for Numerical Relativity
- Supermassive recoil velocities for binary black-hole mergers with antialigned spins
- Spin Flips and Precession in Black-Hole-Binary Mergers
- Hangup Kicks: Still Larger Recoils by Partial Spin/Orbit Alignment of Black-Hole Binaries
- Relativistic Magnetohydrodynamics In Dynamical Spacetimes: Numerical Methods And Tests
- A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
- Numerical relativity simulations of binary neutron stars
- Covariant formulations of BSSN and the standard gauge
- Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits
- Numerical Relativity in Spherical Polar Coordinates: Evolution Calculations with the BSSN Formulation
- Where do moving punctures go?
- BSSN equations in spherical coordinates without regularization: vacuum and non-vacuum spherically symmetric spacetimes
- Analytical Representation of a Black Hole Puncture Solution
- Numerical hydrodynamics in general relativity
- The NINJA-2 project: Detecting and characterizing gravitational waveforms modelled using numerical binary black hole simulations
- General relativistic hydrodynamics in curvilinear coordinates
- Ultrarelativistic fluid dynamics
- Collapse of Nonlinear Gravitational Waves in Moving-Puncture Coordinates
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- Numerical relativity in spherical coordinates with the Einstein Toolkit
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- Critical phenomena in the gravitational collapse of electromagnetic waves
- Aspherical deformations of the Choptuik spacetime
- Critical phenomena in the aspherical gravitational collapse of radiation fluids
- A cosmologically motivated reference formulation of numerical relativity
- Shock-avoiding slicing conditions: tests and calibrations
- Critical gravitational collapse with angular momentum
- Critical gravitational collapse with angular momentum II: soft equations of state
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- Accretion onto black holes inside neutron stars with piecewise-polytropic equations of state: analytic and numerical treatments
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