Black hole evolution by spectral methods

Kidder, Lawrence E.; Scheel, Mark A.; Teukolsky, Saul A.; Carlson, Eric D.; Cook, G.G.

doi:10.1103/physrevd.62.084032

Cited by 103 publications

(129 citation statements)

References 46 publications

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“…In our evolution code, SpEC [57][58][59][60][61][62][63][64][65][66], we use a mixed spectral-finite-difference approach to solving the Einstein field equations coupled to general relativistic hydrodynamics equations. The equations for the space-time metric g μν are solved on a spectral grid, while the fluid equations are solved on a finite difference grid, using a high-resolution shock-capturing scheme.…”

Section: A Evolution Codementioning

confidence: 99%

Binary neutron stars with arbitrary spins in numerical relativity

et al. 2015

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We present a code to construct initial data for binary neutron star systems in which the stars are rotating. Our code, based on a formalism developed by Tichy, allows for arbitrary rotation axes of the neutron stars and is able to achieve rotation rates near rotational breakup. We compute the neutron star angular momentum through quasilocal angular momentum integrals. When constructing irrotational binary neutron stars, we find a very small residual dimensionless spin of ∼2 × 10 −4 . Evolutions of rotating neutron star binaries show that the magnitude of the stars' angular momentum is conserved, and that the spin and orbit precession of the stars is well described by post-Newtonian approximation. We demonstrate that orbital eccentricity of the binary neutron stars can be controlled to ∼0.1%. The neutron stars show quasinormal mode oscillations at an amplitude which increases with the rotation rate of the stars.

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Section: A Evolution Codementioning

confidence: 99%

Binary neutron stars with arbitrary spins in numerical relativity

et al. 2015

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“…Their derivation, and the notation used, is based on [18] and [19], with the addition of terms containing the potential.…”

Section: The Equationsmentioning

confidence: 99%

Scalar field confinement as a model for accreting systems

Megevand

Olabarrieta

Lehner

2007

Class. Quantum Grav.

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We investigate the possibility to localize scalar field configurations as a model for black hole accretion. We analyze and resolve difficulties encountered when localizing scalar fields in General Relativity. We illustrate this ability with a simple spherically symmetric model which can be used to study features of accreting shells around a black hole. This is accomplished by prescribing a scalar field with a coordinate dependent potential. Numerical solutions to the Einstein-Klein-Gordon equations are shown, where a scalar filed is indeed confined within a region surrounding a black hole. The resulting spacetime can be described in terms of simple harmonic time dependence.

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“…We implemented Einstein equations in 1+1 dimensions as described in [21,22] with fourth order accurate derivative operators at interior points (suitably modified near boundary points as dictated by the SBP requirement) and a fourth order Runge-Kutta update scheme in time. We adopt unperturbed initial data corresponding to Schwarzschild in ingoing Eddington Finkelstein coordinates with an analytically given shift and the free part of the densitized lapse function.…”

Section: Spherically Symmetric Spacetimementioning

confidence: 99%

AMR, stability and higher accuracy

Lehner¹,

Liebling²,

Reula³

2006

Class. Quantum Grav.

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Efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second order accurate adaptive mesh refinement or on defining higher order accurate differences and update schemes. Here, we argue for the combination, that is a higher order accurate adaptive scheme. This combines the power that adaptive gridding techniques provide to resolve fine scales (in addition to a more efficient use of resources) together with the higher accuracy furnished by higher order schemes when the solution is adequately resolved. To define a convenient higher order adaptive mesh refinement scheme, we discuss a few different modifications of the standard, second order accurate approach of Berger and Oliger. Applying each of these methods to a simple model problem, we find these options have unstable modes. However, a novel approach to dealing with the grid boundaries introduced by the adaptivity appears stable and quite promising for the use of high order operators within an adaptive framework.

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Black hole evolution by spectral methods

Cited by 103 publications

References 46 publications

Binary neutron stars with arbitrary spins in numerical relativity

Binary neutron stars with arbitrary spins in numerical relativity

Scalar field confinement as a model for accreting systems

AMR, stability and higher accuracy

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