We provide a detailed analysis of several aspects the turduckening technique for evolving black holes. At analytical level we study constraint propagation general family BSSN-type formulation Einstein's field equations and identify under what conditions turducken procedure is rigorously justified violations will propagate to outside present high-resolution spherically symmetric studies which verify our predictions. Then three dimensional simulations single distorted holes using different...

[Abridged] We propose a solution to the problem of quickly and accurately predicting gravitational waveforms within any given physical model. The method is relevant for both real-time applications in more traditional scenarios where generation using standard methods can be prohibitively expensive. Our approach based on three offline steps resulting an accurate reduced-order model that used as surrogate true/fiducial waveform family. First, set m parameter values determined greedy algorithm...

Simulating a binary black hole coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. Using reduced order modeling techniques, we construct an accurate surrogate model, which evaluated in millisecond second, for numerical relativity (NR) waveforms from nonspinning coalescences with mass ratios [1, 10] and durations corresponding about 15 orbits before merger. We assess the model's uncertainty show that our strategy predicts...

Inferring the astrophysical parameters of coalescing compact binaries is a key science goal upcoming advanced LIGO-Virgo gravitational-wave detector network and, more generally, astronomy. However, current approaches to parameter estimation for these detectors require computationally expensive algorithms. Therefore, there pressing need new, fast, and accurate Bayesian inference techniques. In this Letter, we demonstrate that reduced order modeling approach enables rapid be performed. By...

We compute the contribution to Lagrangian from leading order (2.5 post-Newtonian) radiation reaction and quadrupolar gravitational waves emitted a binary system using effective field theory (EFT) approach of Goldberger Rothstein. use an initial value formulation underlying (quantum) framework implement retarded boundary conditions describe these real-time dissipative processes. also demonstrate why usual scattering formalism quantum inadequately accounts for these. The methods discussed here...

We introduce a reduced basis approach as new paradigm for modeling, representing and searching gravitational waves. construct waveform catalogs non-spinning compact binary coalescences, we find that accuracies of 99% 99.999% the method generates factor about $10-10^5$ fewer templates than standard placement methods. The continuum waves can be represented by finite comparatively basis. is robust under variations in noise detectors, implying only single catalog needs to generated.

We derive a geometrical version of the Regge-Wheeler and Zerilli equations, which allows us to study gravitational perturbations on an arbitrary spherically symmetric slicing Schwarzschild black hole. explain how obtain gauge-invariant part metric from amplitudes obeying our generalized vice-versa. also give general expression for radiated energy at infinity, establish relation between equations Teukolsky formalism. The results presented in this paper are expected be useful close-limit...

One of the main bottlenecks in gravitational wave (GW) astronomy is high cost performing parameter estimation and GW searches on fly. We propose a novel technique based reduced order quadratures (ROQs), an application data-specific quadrature rule, to perform fast accurate likelihood evaluations. These are dominant Markov chain Monte Carlo algorithms, which widely employed studies, so ROQs offer new way accelerate estimation. illustrate our approach using four-dimensional burst model...

We discuss an equivalence between the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of Einstein evolution equations, a subfamiliy Kidder--Scheel--Teukolsky formulation, and other strongly or symmetric hyperbolic first order systems with fixed shift densitized lapse. This allows us to show under which conditions BSSN system is, in sense be discussed, hyperbolic. desirable property may account part for empirically observed better behavior numerical evolutions involving black holes.

We describe a generic infrastructure for time evolution simulations in numerical relativity using multiple grid patches. After motivation of this approach, we discuss the relative advantages global and patch-local tensor bases. both our multi-patch scheme, comment on adaptive integrators parallelization. also various patch system topologies that provide spherical outer and/or inner boundaries. employ penalty inter-patch boundary conditions, demonstrate stability accuracy three-dimensional...

to turducken (turduckens, turduckening, turduckened, turduckened) [math.]: To stuff a black hole. We analyze and apply an alternative hole excision based on smoothing the interior of holes with arbitrary initial data, solving vacuum Einstein evolution equations everywhere. By deriving constraint propagation system for our hyperbolic formulation BSSN we rigorously prove that constraints propagate causally so any violations introduced inside cannot affect exterior spacetime. present evolutions...

We present numerical results from three-dimensional evolutions of scalar perturbations Kerr black holes. Our simulations make use a high-order accurate multiblock code which naturally allows for adapted grids and smooth inner (excision) outer boundaries. focus on the quasinormal ringing phase, presenting systematic method extraction mode frequencies amplitudes comparing our against perturbation theory. The detection single in ringdown waveform measurement mass spin hole; multimode would...

Using recently developed efficient symbolic manipulations tools, we present a general gauge-invariant formalism to study arbitrary radiative ($l\ensuremath{\ge}2$) second-order perturbations of Schwarzschild black hole. In particular, construct the Zerilli and Regge-Wheeler equations under presence any two first-order modes, reconstruct perturbed metric in terms master scalars, compute radiated energy at null infinity. The results this paper enable systematic studies generic spacetime,...

This is the first paper in a series aimed to implement boundary conditions consistent with constraints' propagation 3D unconstrained numerical relativity. Here we consider spherically symmetric black hole spacetimes vacuum or minimally coupled scalar field, within Einstein-Christoffel (EC) hyperbolic formulation of Einstein's equations. By exploiting characteristic main variables and constraints, are able single out only free modes at outer for these problems. In case mode exists which...

We discuss finite difference techniques for hyperbolic equations in non-trivial domains, as those that arise when simulating black hole spacetimes. In particular, we construct dissipative and operators satisfy the {\it summation by parts} property domains with excised multiple cubic regions. This can be used to derive semi-discrete energy estimates associated initial-boundary value problem which turn prove numerical stability.

The need to smoothly cover a computational domain of interest generically requires the adoption several grids. To solve given problem under this grid structure, one must ensure suitable transfer information among different grids involved. In work, we discuss technique that allows construct finite-difference schemes arbitrary high order which are guaranteed satisfy linear numerical and strict stability. method relies on use difference operators satisfying summation by parts penalty terms...

We present two methods to include the asymptotic domain of a background spacetime in null directions for numerical solutions evolution equations so that both radiation extraction problem and outer boundary are solved. The first method is based on geometric conformal approach, second coordinate approach. apply these case massless scalar wave equation Kerr spacetime. Our designed allow existing codes reach radiative zone by including future infinity computational with relatively minor...

Abstract We present an introduction to some of the state art in reduced order and surrogate modeling gravitational-wave (GW) science. Approaches that we cover include principal component analysis, proper orthogonal (singular value) decompositions, basis approach, empirical interpolation method, quadratures, compressed likelihood evaluations. divide review into three parts: representation/compression known data, predictive models, data analysis. The targeted audience is practitioners GW...

We present a new fully first-order strongly hyperbolic representation of the Baumgarte-Shapiro-Shibata-Nakamura formulation Einstein's equations with optional constraint damping terms. describe characteristic fields system, discuss its hyperbolicity properties, and two numerical implementations simulations: one using finite differences, adaptive mesh refinement, and, in particular, binary black holes, another discontinuous Galerkin method spherical symmetry. The results this paper constitute...

Outer boundary conditions for strongly and symmetric hyperbolic formulations of 3D Einstein's field equations with a live gauge condition are discussed. The have the property that they ensure constraint propagation control in sense made precise this article physical degrees freedom at boundary. We use Fourier–Laplace transformation techniques to find necessary well posedness resulting initial-boundary value problem integrate three-dimensional nonlinear using finite-differencing code. obtain...

We present a method for extracting gravitational waves from numerical spacetimes which generalizes and refines one of the standard methods based on Regge--Wheeler--Zerilli perturbation formalism. [abridged] then fully nonlinear three-dimensional evolutions distorted Schwarzschild black hole in Kerr--Schild coordinates with an odd parity analyze improvement we gain our generalized wave extraction, comparing new to one. find that, even observers as far out $R=80 M$--which is larger than what...