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 zdirection this would give the plus solution

hxx = hyy = f(t ± z),hxy = hxz = hyz = hzz = 0

and the cross solution

hxy = hyx = f(t ± z),hyz = hxx = hyy = hzz = 0

This thorn implements the plus solution, with the waveform f(t ± 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:

f(t,x,y,z) = Aine(kipxi+ω p(tra))2 cos(kixi + ωt) + A oute(kipxiω p(tra))2 cos(kixi ωt)

and

gxx = 1 + f[cos2ϕ cos𝜃 sin2ϕ] gxy = fsin2𝜃sinϕcosϕ gxz = fsin𝜃cos𝜃sinϕ gyy = 1 + f[sin2ϕ cos2𝜃cos2ϕ] gyz = fsin𝜃cos𝜃cosϕ gzz = 1 fsin2𝜃

The extrinsic curvature is then calculated from

Kij = 1 2αġij (1)

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




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



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

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

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