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Provides gravitational wave solutions to the linearized Einstein equations

There are two different linearized initial data sets provided, plane waves and Teukolsky waves.

A full description of plane waves can be found in the PhD Thesis of Malcolm Tobias, The Numerical Evolution of Gravitational Waves, which can be found at http://wugrav.wustl.edu/Papers/Thesis97/Thesis97.html.

Plane waves travelling in arbitrary directions can be specified. For these plane waves the TT gauge is assumed (the metric perturbations are transverse to the direction of propagation, and the metric is traceless). In the case of waves travelling along the \(z-\)direction this would give the plus solution

and the cross solution

This thorn implements the plus solution, with the waveform \(f(t\pm z)\) having the form of a Gaussian modulated sine function. Now working with a general direction of propagation \(k\) we have the plane wave solution:

and

\begin {eqnarray*} g_{xx}&=& 1 + f[\cos ^2\phi - \cos ^\theta \sin ^2\phi ] \\ g_{xy}&=& - f \sin ^2 \theta \sin \phi \cos \phi \\ g_{xz} &=& f \sin \theta \cos \theta \sin \phi \\ g_{yy} &=& 1+f [\sin ^2\phi - cos^2\theta \cos ^2\phi ] \\ g_{yz} &=& f \sin \theta \cos \theta \cos \phi \\ g_{zz} &=& 1-f\sin ^2\theta \end {eqnarray*}

The extrinsic curvature is then calculated from \begin {equation} K_{ij} = - \frac {1}{2\alpha } \dot {g}_{ij} \end {equation}

Teukolsky waves are quadrupole wave solutions to the linearized Einstein equations. For a full description, see: PRD 26:745 (1982).

The extrinsic curvature is initialized assuming the initial lapse is one.

amplitude | Scope: private | REAL |

Description: Amplitude of the wave: both for teuk and plane
| ||

Range | Default: 0.001 | |

0: | positive amplitude
| |

mvalue | Scope: private | INT |

Description: m value for teukwaves waves: integer from -2 to 2
| ||

Range | Default: (none) | |

-2:2 | implemented : m = -2..2
| |

packet | Scope: private | KEYWORD |

Description: Packet for teukwaves: eppley,evans,square
| ||

Range | Default: eppley | |

eppley | Eppley type
| |

evans | Evans type
| |

square | Square type
| |

parity | Scope: private | KEYWORD |

Description: Parity for teukwaves: even or odd
| ||

Range | Default: even | |

even | even parity
| |

odd | odd parity
| |

teuk_no_vee | Scope: private | KEYWORD |

Description: Initialize Teuk. waves with V=0?
| ||

Range | Default: no | |

no | Bona Masso setting
| |

yes | Bona Masso setting
| |

wavecenter | Scope: private | REAL |

Description: linears waves thingie
| ||

Range | Default: 0.0 | |

: | ||

wavelength | Scope: private | REAL |

Description: linearwaves wave length
| ||

Range | Default: 2.0 | |

0: | positive wavelength
| |

wavephi | Scope: private | REAL |

Description: Phi angle for planewaves
| ||

Range | Default: 0.0 | |

: | ||

wavepulse | Scope: private | REAL |

Description: planewaves thingy for the gaussian pulse
| ||

Range | Default: 1.0 | |

0: | positive pulse
| |

wavesgoing | Scope: private | KEYWORD |

Description: in and outgoing waves...
| ||

Range | Default: both | |

in | Ingoing wave
| |

out | Outgoing wave
| |

both | In and outgoing wave
| |

wavetheta | Scope: private | REAL |

Description: Theta angle for planewaves
| ||

Range | Default: 0.0 | |

: | ||

conformal_storage | Scope: shared from STATICCONFORMAL | KEYWORD |

Implements:

idlinearwaves

Inherits:

admbase

staticconformal

grid

This section lists all the variables which are assigned storage by thorn EinsteinInitialData/IDLinearWaves. Storage can either last for the duration of the run (Always means that if this thorn is activated storage will be assigned, Conditional means that if this thorn is activated storage will be assigned for the duration of the run if some condition is met), or can be turned on for the duration of a schedule function.

NONE

CCTK_PARAMCHECK (conditional)

idlinearwaves_paramchecker

check that the metric_type is recognised

Language: | c | |

Options: | global | |

Type: | function | |

ADMBase_InitialData (conditional)

idlinearwaves_planewaves

construct linear planewave initial data

Language: | fortran | |

Type: | function | |

CCTK_PARAMCHECK (conditional)

idlinearwaves_paramchecker

check that the metric_type is recognised

Language: | c | |

Options: | global | |

Type: | function | |

ADMBase_InitialData (conditional)

idlinearwaves_standwaves

construct linear planewave initial data

Language: | fortran | |

Type: | function | |

CCTK_PARAMCHECK (conditional)

idlinearwaves_paramchecker

check that the metric_type is recognised

Language: | c | |

Options: | global | |

Type: | function | |

ADMBase_InitialData (conditional)

idlinearwaves_teukwaves

construct linear teukolsky wave initial data

Language: | fortran | |

Type: | function | |

Writes: | admbase::metric(everywhere) | |

admbase::curv(everywhere) | ||

CCTK_PARAMCHECK (conditional)

idlinearwaves_paramchecker

check that the metric_type is recognised

Language: | c | |

Options: | global | |

Type: | function | |

ADMBase_InitialData (conditional)

idlinearwaves_sineplanewaves

construct linear plane wave initial data

Language: | fortran | |

Type: | function | |