SENR /NRPy + : Numerical relativity in singular curvilinear coordinate systems
Abstract
We report on a new opensource, userfriendly numerical relativity code package called SENR /NRPy + . Our code extends previous implementations of the BSSN referencemetric formulation to a much broader class of curvilinear coordinate systems, making it ideally suited to modeling physical configurations with approximate or exact symmetries. In the context of modeling black hole dynamics, it is orders of magnitude more efficient than other widely used opensource numerical relativity codes. NRPy + provides a Pythonbased interface in which equations are written in natural tensorial form and output at arbitrary finite difference order as highly efficient C code, putting complex tensorial equations at the scientist's fingertips without the need for an expensive software license. SENR provides the algorithmic framework that combines the C codes generated by NRPy + into a functioning numerical relativity code. We validate against two other established, stateoftheart codes, and achieve excellent agreement. For the first time—in the context of moving puncture black hole evolutions—we demonstrate nearly exponential convergence of constraint violation and gravitational waveform errors to zero as the order of spatial finite difference derivatives is increased, while fixing the numerical grids at moderate resolution in a singular coordinate system. Such behavior outside the horizons is remarkable, as numerical errors do not converge to zero near punctures, and all points along the polar axis are coordinate singularities. The formulation addresses such coordinate singularities via cellcentered grids and a simple change of basis that analytically regularizes tensor components with respect to the coordinates. Future plans include extending this formulation to allow dynamical coordinate grids and bisphericallike distribution of points to efficiently capture orbiting compact binary dynamics.
 Publication:

Physical Review D
 Pub Date:
 March 2018
 DOI:
 10.1103/PhysRevD.97.064036
 arXiv:
 arXiv:1712.07658
 Bibcode:
 2018PhRvD..97f4036R
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 23 pages, 7 figures, matches published version