xx IDLinearWaves

IDLinearWaves

Gabrielle Allen, Tom Goodale, Gerd Lanfermann, Joan Masso, Mark Miller, Malcolm Tobias, Paul Walker

Date

Abstract

Provides gravitational wave solutions to the linearized Einstein equations

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

2 Plane 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 direction this would give the plus solution

. h_{xx} = −h_{yy} = f(t ± z), h_{xy} = h_{xz} = h_{yz} = h_{zz} = 0

and the cross solution

. h_{xy} = h_{yx} = f(t ± z), h_{yz} = h_{xx} = h_{yy} = h_{zz} = 0

This thorn implements the plus solution, with the waveform having the form of a Gaussian modulated sine function. Now working with a general direction of propagation we have the plane wave solution:

. f(t, x, y, z) = A_{in}e^{−(k_{i}^{p}x^{i}+ω_{p}(t−r_{a}))^{2}} cos(k_{i}x^{i} + ωt) + A_{out}e^{−(k_{i}^{p}x^{i}−ω_{p}(t−r_{a}))^{2}} cos(k_{i}x^{i} − ωt) and

The extrinsic curvature is then calculated from

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

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

5 Parameters

11amplitude 10Scope: privatex01 REAL

11Description: Amplitude of the wave: both for teuk and plane

11 Range 10 x01 Default: 0.001
110:  10positive amplitude

11

11mvalue  10Scope: privatex01  INT

11Description: m value for teukwaves waves: integer from -2 to 2

11 Range 10 x01 Default: (none)
11-2:2  10implemented : m = -2..2

11

11packet  10Scope: privatex01  KEYWORD

11Description: Packet for teukwaves: eppley,evans,square

11 Range 10 x01 Default: eppley
11eppley  10Eppley type
11evans  10Evans type
11square  10Square type

11parity  10Scope: privatex01  KEYWORD

11Description: Parity for teukwaves: even or odd

11 Range 10 x01 Default: even
11even  10even parity
11odd  10odd parity

11

11teukxnoxvee  10Scope: privatex01  KEYWORD

11Description: Initialize Teuk. waves with V=0?

11 Range 10 x01 Default: no
11no  10Bona Masso setting
11yes  10Bona Masso setting

11

11wavecenter  10Scope: privatex01  REAL

11Description: linears waves thingie

11  Range  10  x01  Default: 0.0

11:  10

11

11wavelength  10Scope: privatex01  REAL

11Description: linearwaves wave length

11 Range 10 x01 Default: 2.0
110:  10positive wavelength

11

11wavephi  10Scope: privatex01  REAL

11Description: Phi angle for planewaves

11  Range  10  x01  Default: 0.0

11:  10

11

11wavepulse  10Scope: privatex01  REAL

11Description: planewaves thingy for the gaussian pulse

11 Range 10 x01 Default: 1.0
110:  10positive pulse

11

11wavesgoing  10Scope: privatex01  KEYWORD

11Description: in and outgoing waves...

11 Range 10 x01 Default: both
11in  10Ingoing wave
11out  10Outgoing wave
11both  10In and outgoing wave

11

11wavetheta  10Scope: privatex01  REAL

11Description: Theta angle for planewaves

11  Range  10  x01  Default: 0.0

11:  10

11

11conformalxstorage 10Scope: shared from STATICCONFORMALx01KEYWORD

11

6 Interfaces General Implements: idlinearwaves

Inherits: admbase staticconformal grid

7 Schedule 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.

Storage NONE

Scheduled Functions

CCTKxPARAMCHECK (conditional) x idlinearwavesxparamchecker x check that the metricxtype is recognised x

11x11Language:11c
11 x 11Options: 11global
11 x 11Type: 11function

11

ADMBasexInitialData (conditional) x idlinearwavesxplanewaves x construct linear planewave initial data

11x11Language:11fortran
11 x 11Type: 11function

11

CCTKxPARAMCHECK (conditional) x idlinearwavesxparamchecker x check that the metricxtype is recognised x

11x11Language:11c
11 x 11Options: 11global
11 x 11Type: 11function

11

ADMBasexInitialData (conditional) x idlinearwavesxstandwaves x construct linear planewave initial data x

11x11Language:11fortran
11 x 11Type: 11function

11

CCTKxPARAMCHECK (conditional) x idlinearwavesxparamchecker x check that the metricxtype is recognised x

11x11Language:11c
11 x 11Options: 11global
11 x 11Type: 11function

11

ADMBasexInitialData (conditional) x idlinearwavesxteukwaves x construct linear teukolsky wave initial data x

11x11Language:11fortran
11 x 11Type: 11function
11 x 11Writes: 11admbase::metric(everywhere)
11 x 11x  11admbase::curv(everywhere)

11

CCTKxPARAMCHECK (conditional) x idlinearwavesxparamchecker x check that the metricxtype is recognised x

11x11Language:11c
11 x 11Options: 11global
11 x 11Type: 11function

11

ADMBasexInitialData (conditional) x idlinearwavesxsineplanewaves x construct linear plane wave initial data x

11x11Language:11fortran
11 x 11Type: 11function