Stability of the puncture method with a generalized Baumgarte-Shapiro-Shibata-Nakamura formulation

Witek, Helvi; Hilditch, David; Sperhake, Ulrich

doi:10.1103/physrevd.83.104041

Cited by 21 publications

(26 citation statements)

References 72 publications

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“…Another modification of the BSSN equations is based on the use of densitized versions of the trace of the extrinsic curvature and the lapse function as well as the traceless part of the extrinsic curvature with mixed indices [497, 795]. Some improvements in simulations of colliding BHs in higher-dimensional spacetimes have been found by careful exploration of the densitization parameter space [791].…”

Section: Numerical Relativitymentioning

confidence: 99%

Exploring New Physics Frontiers Through Numerical Relativity

et al. 2015

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The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein’s equations — along with some spectacular results — in various setups.We review techniques for solving Einstein’s equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology.

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Section: Numerical Relativitymentioning

confidence: 99%

Exploring New Physics Frontiers Through Numerical Relativity

et al. 2015

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“…The extension to higher-dimensional spacetimes is a topic of current investigations [337,338,339]. The first numerical results concerning low-energy collisions have been reported last year [339,340], initial data for boosted BH binaries have been constructed using an extended puncture approach in [341,342] and some results for high-energy collisions have been presented in [343]. AdS/CFT and holography.…”

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confidence: 99%

Numerical simulations of black-hole binaries and gravitational wave emission

Sperhake

Berti

Cardoso

2013

Comptes Rendus. Physique

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We review recent progress in numerical relativity simulations of black-hole (BH) spacetimes. Following a brief summary of the methods employed in the modeling, we summarize the key results in three major areas of BH physics: (i) BHs as sources of gravitational waves (GWs), (ii) astrophysical systems involving BHs, and (iii) BHs in high-energy physics. We conclude with a list of the most urgent tasks for numerical relativity in these three areas.

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“…[440] presents a stability analysis around flat spacetime for a family of generalized BSSN-type formulations, along with numerical experiments, which include binary black-hole inspirals.…”

Section: Spatial Approximations: Finite Differencesmentioning

confidence: 99%

Continuum and Discrete Initial-Boundary Value Problems and Einstein’s Field Equations

Sarbach

Tiglio

2012

Living Rev. Relativ.

150

168

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Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black-hole problem within Einstein’s theory of gravitation, in which one computes the gravitational radiation emitted from the inspiral of the two black holes, merger and ringdown. Powerful mathematical tools can be used to establish qualitative statements about the solutions, such as their existence, uniqueness, continuous dependence on the initial data, or their asymptotic behavior over large time scales. However, one is often interested in computing the solution itself, and unless the partial differential equation is very simple, or the initial data possesses a high degree of symmetry, this computation requires approximation by numerical discretization. When solving such discrete problems on a machine, one is faced with a finite limit to computational resources, which leads to the replacement of the infinite continuum domain with a finite computer grid. This, in turn, leads to a discrete initial-boundary value problem. The hope is to recover, with high accuracy, the exact solution in the limit where the grid spacing converges to zero with the boundary being pushed to infinity.The goal of this article is to review some of the theory necessary to understand the continuum and discrete initial boundary-value problems arising from hyperbolic partial differential equations and to discuss its applications to numerical relativity; in particular, we present well-posed initial and initial-boundary value formulations of Einstein’s equations, and we discuss multi-domain high-order finite difference and spectral methods to solve them.

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Stability of the puncture method with a generalized Baumgarte-Shapiro-Shibata-Nakamura formulation

Cited by 21 publications

References 72 publications

Exploring New Physics Frontiers Through Numerical Relativity

Exploring New Physics Frontiers Through Numerical Relativity

Numerical simulations of black-hole binaries and gravitational wave emission

Continuum and Discrete Initial-Boundary Value Problems and Einstein’s Field Equations

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