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We report on a new open-source, user-friendly numerical relativity code package called SENR/NRPy+. Our code extends previous implementations of the BSSN reference-metric 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 open-source numerical relativity codes. NRPy+ provides a Python-based 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, state-of-the-art 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 cell-centered 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 bispherical-like distribution of points to efficiently capture orbiting compact binary dynamics. [ABSTRACT FROM AUTHOR]

We use fully nonlinear numerical relativity techniques to estimate the maximum gravitational radiation emitted by high energy head-on collisions of nonspinning, equal-mass black holes. Our simulations include improvements in the construction of initial data, subsequent full numerical evolutions, and the computation of waveforms at infinity. The new initial data significantly reduce the spurious radiation content, allowing for initial speeds much closer to the speed of light, i.e., v ~ 0.99c. Using these new techniques, we estimate the maximum radiated energy from head-on collisions to be Emax/MADM = 0.13 ± 0.01. This value differs from the second-order perturbative (0.164) and zero-frequency-limit (0.17) analytic computations but is close to those obtained by thermodynamic arguments (0.134) and by previous numerical estimates (0.14 ± 0.03). [ABSTRACT FROM AUTHOR]

Numerical relativity codes that do not make assumptions on spatial symmetries most commonly adopt Cartesian coordinates. While these coordinates have many attractive features, spherical coordinates are much better suited to take advantage of approximate symmetries in a number of astrophysical objects, including single stars, black holes, and accretion disks. While the appearance of coordinate singularities often spoils numerical relativity simulations in spherical coordinates, especially in the absence of any symmetry assumptions, it has recently been demonstrated that these problems can be avoided if the coordinate singularities are handled analytically. This is possible with the help of a reference-metric version of the Baumgarte-Shapiro-Shibata-Nakamura formulation together with a proper rescaling of tensorial quantities. In this paper we report on an implementation of this formalism in the Einstein Toolkit. We adapt the Einstein Toolkit infrastructure, originally designed for Cartesian coordinates, to handle spherical coordinates, by providing appropriate boundary conditions at both inner and outer boundaries. We perform numerical simulations for a disturbed Kerr black hole, extract the gravitational wave signal, and demonstrate that the noise in these signals is orders of magnitude smaller when computed on spherical grids rather than Cartesian grids. With the public release of our new Einstein Toolkit thorns, our methods for numerical relativity in spherical coordinates will become available to the entire numerical relativity community. [ABSTRACT FROM AUTHOR]

We demonstrate that numerical relativity codes based on the "moving punctures" formalism are capable of evolving nearly maximally spinning black hole binaries. We compare a new evolution of an equal-mass, aligned-spin binary with dimensionless spin χ = 0.99 using puncture-based data with recent simulations of the SXS Collaboration. We find that the overlap of our new waveform with the published results of the SXS Collaboration is larger than 0.999. To generate our new waveform, we use the recently introduced HiSpID puncture data, the CCZ4 evolution system, and a modified lapse condition that helps keep the horizon radii reasonably large. [ABSTRACT FROM AUTHOR]