Extracting Gravitational Waves and Other Quantities from Numerical Spacetimes

Gabrielle Allen

Abstract

1 Introduction

Thorn Extract calculates first order gauge invariant waveforms from a numerical spacetime, under the basic assumption that, at the spheres of extract the spacetime is approximately Schwarzschild. In addition, other quantities such as mass, angular momentum and spin can be determined.

This thorn should not be used blindly, it will always return some waveform, however it is up to the user to determine whether this is the appropriate expected first order gauge invariant waveform.

2 Physical System

2.1 Wave Forms

Assume a spacetime gαβ which can be written as a Schwarzschild background gαβSchwarz with perturbations hαβ:

gαβ = gαβSchwarz + h αβ (1)

with

{gαβSchwarz}(t,r,𝜃,ϕ) = S 0 0 0 0 S1 0 0 0 0 r2 0 0 0 0 r2 sin2𝜃 S(r) = 12M r (2)

The 3-metric perturbations γij can be decomposed using tensor harmonics into γijlm(t,r) where

γij(t,r,𝜃,ϕ) = l=0 m=llγ ijlm(t,r)

and

γij(t,r,𝜃,ϕ) = k=06p k(t,r)V k(𝜃,ϕ)

where {V k} is some basis for tensors on a 2-sphere in 3-D Euclidean space. Working with the Regge-Wheeler basis (see Section 6) the 3-metric is then expanded in terms of the (six) standard Regge-Wheeler functions {c1×lm,c2×lm,h1+lm,H2+lm,K+lm,G+lm} [19][16]. Where each of the functions is either odd (×) or even (+) parity. The decomposition is then written

γijlm = c 1×lm(ê 1)ijlm + c 2×lm(ê 2)ijlm + h1+lm(f̂ 1)ijlm + A2H 2+lm(f̂ 2)ijlm + R2K+lm(f̂ 3)ijlm + R2G+lm(f̂ 4)ijlm (3)

which we can write in an expanded form as

γrrlm = A2H 2+lmY lm (4) γr𝜃lm = c 1×lm 1 sin𝜃Y lm,ϕ + h1+lmY lm,𝜃 (5) γrϕlm = c 1×lm sin𝜃Y lm,𝜃 + h1+lmY lm,ϕ (6) γ𝜃𝜃lm = c 2×lm 1 sin𝜃(Y lm,𝜃ϕ cot𝜃Y lm,ϕ) + R2K+lmY lm + R2G+lmY lm,𝜃𝜃 (7) γ𝜃ϕlm = c 2×lm sin𝜃1 2 Y lm,𝜃𝜃 cot𝜃Y lm,𝜃 1 sin2𝜃Y lm + R2G+lm(Y lm,𝜃ϕ cot𝜃Y lm,ϕ) (8) γϕϕlm = sin𝜃c 2×lm(Y lm,𝜃ϕ cot𝜃Y lm,ϕ) + R2K+lm sin2𝜃Y lm + R2G+lm(Y lm,ϕϕ + sin𝜃cos𝜃Y lm,𝜃) (9)

A similar decomposition allows the four gauge components of the 4-metric to be written in terms of three even-parity variables {H0,H1,h0} and the one odd-parity variable {c0}

gttlm = N2H 0+lmY lm (10) gtrlm = H 1+lmY lm (11) gt𝜃lm = h 0+lmY lm,𝜃 c0×lm 1 sin𝜃Y lm,ϕ (12) gtϕlm = h 0+lmY lm,ϕ + c0×lm sin𝜃Y lm,𝜃 (13)

Also from gtt = α2 + βiβi we have

αlm = 1 2NH0+lmY lm (14)

It is useful to also write this with the perturbation split into even and odd parity parts:

gαβ = gαβbackground + l,mgαβlm,odd + l,mgαβlm,even

where (dropping some superscripts)

{gαβodd} = 00 c0 1 sin 𝜃Y lm,ϕ c0 sin𝜃Y lm,𝜃 . 0 c1 1 sin 𝜃Y lm,ϕ c1 sin𝜃Y lm,𝜃 . .c2 1 sin 𝜃(Y lm,𝜃ϕ cot𝜃Y lm,ϕ)c21 2 1 sin 𝜃Y lm,ϕϕ + cos𝜃Y lm,𝜃 sin𝜃Y lm,𝜃𝜃 . . . c2(sin𝜃Y lm,𝜃ϕ + cos𝜃Y lm,ϕ) {gαβeven} = N2H0Y lm H1Y lm h0Y lm,𝜃 h0Y lm,ϕ . A2H2Y lm h1Y lm,𝜃 h1Y lm,ϕ . . R2KY lm + r2GY lm,𝜃𝜃 R2(Y lm,𝜃ϕ cot𝜃Y lm,ϕ) . . . R2Ksin2𝜃Y lm + R2G(Y lm,ϕϕ + sin𝜃cos𝜃Y lm,𝜃)

Now, for such a Schwarzschild background we can define two (and only two) unconstrained gauge invariant quantities Qlm× = Qlm×(c1×lm,c2×lm) and Qlm+ = Qlm+(K+lm,G+lm,H2+lm,h1+lm), which from [3] are

Qlm× = 2(l + 2)! (l 2)! c1×lm + 1 2 rc2×lm 2 rc2×lm S r (15) Qlm+ = 1 Λ 2(l 1)(l + 2) l(l + 1) (4rS2k 2 + l(l + 1)rk1) (16) 1 Λ 2(l 1)(l + 2) l(l + 1) l(l + 1)S(r2 rG+lm 2h 1+lm) + 2rS(H 2+lm r rK+lm) + ΛrK+lm (17)

where

k1 = K+lm + S r (r2 rG+lm 2h 1+lm) (18) k2 = 1 2S H2+lm r rk1 1 M rSk1 + S12 r(r2S12 rG+lm 2S12h 1+lm) (19) 1 2S H2 rK,r r 3M r 2MK (20)

NOTE: These quantities compare with those in Moncrief [16] by

Moncriefs odd parity Q: Qlm× = 2(l + 2)! (l 2)! Q Moncriefs even parity Q: Qlm+ = 2(l 1)(l + 2) l(l + 1) Q

Note that these quantities only depend on the purely spatial Regge-Wheeler functions, and not the gauge parts. (In the Regge-Wheeler and Zerilli gauges, these are just respectively (up to a rescaling) the Regge-Wheeler and Zerilli functions). These quantities satisfy the wave equations

(t2 r2)Q lm× + S l(l + 1) r2 6M r3 Qlm× = 0 (t2 r2)Q lm+ + S 1 Λ2 72M3 r5 12M r3 (l 1)(l + 2) 1 3M r + l(l 1)(l + 1)(l + 2) r2Λ Qlm+ = 0

where

Λ = (l 1)(l + 2) + 6Mr r = r + 2Mln(r2M 1)

3 Numerical Implementation

The implementation assumes that the numerical solution, on a Cartesian grid, is approximately Schwarzshild on the spheres of constant r = (x2 + y2 + z2) where the waveforms are extracted. The general procedure is then:

3.1 Project onto Spheres of Constant Radius

This is performed by interpolating the metric components, and if needed the conformal factor, onto the spheres. Although 2-spheres are hardcoded, the source code could easily be changed here to project onto e.g. 2-ellipsoids.

3.2 Calculate Radial Transformation

The areal coordinate r̂ of each sphere is calculated by

r̂ = r̂(r) = 1 4πγ𝜃𝜃 γϕϕd𝜃dϕ12 (21)

from which

dr̂ dη = 1 16πr̂γ𝜃𝜃,ηγϕϕ + γ𝜃𝜃γϕϕ,η γ𝜃𝜃 γϕϕ d𝜃dϕ (22)

Note that this is not the only way to combine metric components to get the areal radius, but this one was used because it gave better values for extracting close to the event horizon for perturbations of black holes.

3.3 Calculate S factor and Mass Estimate

S(r̂) = r̂ r 2γrrd𝜃dϕ (23)
M(r̂) = r̂1 S 2 (24)

3.4 Calculate Regge-Wheeler Variables

c1×lm = 1 l(l + 1) γr̂ϕY lm,𝜃 γr̂𝜃Y lm,ϕ sin𝜃 dΩ c2×lm = 2 l(l + 1)(l 1)(l + 2) 1 sin2𝜃γ𝜃𝜃 + 1 sin4𝜃γϕϕ (sin𝜃Y lm,𝜃ϕ cos𝜃Y lm,ϕ) + 1 sin𝜃γ𝜃ϕ(Y lm,𝜃𝜃 cot𝜃Y lm,𝜃 1 sin2𝜃Y lm,ϕϕ)dΩ h1+lm = 1 l(l + 1) γr̂𝜃Y lm,𝜃 + 1 sin2𝜃γr̂ϕY lm,ϕdΩ H2+lm = Sγr̂r̂Y lmdΩ K+lm = 1 2r̂2 γ𝜃𝜃 + 1 sin2𝜃γϕϕ Y lmdΩ + 1 2r̂2(l 1)(l + 2)γ𝜃𝜃 γϕϕ sin2𝜃 Y lm,𝜃𝜃 cot𝜃Y lm,𝜃 1 sin2𝜃Y lm,ϕϕ + 4 sin2𝜃γ𝜃ϕ(Y lm,𝜃ϕ cot𝜃Y lm,ϕ)dΩ G+lm = 1 r̂2l(l + 1)(l 1)(l + 2) γ𝜃𝜃 γϕϕ sin2𝜃 Y lm,𝜃𝜃 cot𝜃Y lm,𝜃 1 sin2𝜃Y lm,ϕϕ + 4 sin2𝜃γ𝜃ϕ(Y lm,𝜃ϕ cot𝜃Y lm,ϕ)dΩ

where

γr̂r̂ = r r̂ r r̂γrr (25) γr̂𝜃 = r r̂γr𝜃 (26) γr̂ϕ = r r̂γrϕ (27)

3.5 Calculate Gauge Invariant Quantities

Qlm× = 2(l + 2)! (l 2)! c1×lm + 1 2 r̂c2×lm 2 r̂c2×lm S r̂ (28) Qlm+ = 1 (l 1)(l + 2) + 6Mr̂ 2(l 1)(l + 2) l(l + 1) (4r̂S2k 2 + l(l + 1)r̂k1) (29)

where

k1 = K+lm + S r̂(r̂2 r̂G+lm 2h 1+lm) (30) k2 = 1 2S[H2+lm r̂ r̂k1 (1 M r̂S)k1 + S12 r̂(r̂2S12 r̂G+lm 2S12h 1+lm (31)

4 Using This Thorn

Use this thorn very carefully. Check the validity of the waveforms by running tests with different resolutions, different outer boundary conditions, etc to check that the waveforms are consistent.

4.1 Basic Usage

4.2 Output Files

Although Extract is really an ANALYSIS thorn, at the moment it is scheduled at POSTSTEP, with the iterations at which output is performed determined by the parameter itout. Output files from Extract are always placed in the main output directory defined by CactusBase/IOUtil.

Output files are generated for each detector (2-sphere) used, and these detectors are identified in the name of each output file by R1, R2, ….

The extension denotes whether coordinate time (ṫl) or proper time (u̇l) is used for the first column.

5 History

Much of the source code for Extract comes from a code written outside of Cactus for extracting waveforms from data generated by the NCSA G-Code for compare with linear evolutions of waveforms extracted from the Cauchy initial data. This work was carried out in collaboration with Karen Camarda and Ed Seidel.

6 Appendix: Regge-Wheeler Harmonics

(ê1)lm = 0 1 sin 𝜃Y lm,ϕ sin𝜃Y lm,𝜃 . 0 0 . 0 0 (ê2)lm = 0 0 0 0 1 sin 𝜃(Y lm,𝜃ϕ cot𝜃Y lm,ϕ) . 0 sin 𝜃 2 [Y lm,𝜃𝜃 cot𝜃Y lm,𝜃 1 sin 2𝜃Y lm,ϕϕ] sin𝜃[Y lm,𝜃ϕ cot𝜃Y lm,ϕ] (f̂1)lm = 0Y lm,𝜃Y lm,ϕ . 0 0 . 0 0 (f̂2)lm = Y lm00 0 00 0 0 0 (f̂3)lm = 0 0 0 0 Y lm 0 0 0 sin2𝜃Y lm (f̂4)lm = 0 0 0 0 Y lm,𝜃𝜃 . 0Y lm,𝜃ϕ cot𝜃Y lm,ϕY lm,ϕϕ + sin𝜃cos𝜃Y lm,𝜃

7 Appendix: Transformation Between Cartesian and Spherical Coordinates

First, the transformations between metric components in (x,y,z) and (r,𝜃,ϕ) coordinates. Here, ρ = x2 + y2 = rsin𝜃,

x r = sin𝜃cosϕ = x r y r = sin𝜃sinϕ = y r z r = cos𝜃 = z r x 𝜃 = rcos𝜃cosϕ = xz ρ y 𝜃 = rcos𝜃sinϕ = yz ρ z 𝜃 = rsin𝜃 = ρ x ϕ = rsin𝜃sinϕ = y y ϕ = rsin𝜃cosϕ = x z ϕ = 0

γrr = 1 r2(x2γ xx + y2γ yy + z2γ zz + 2xyγxy + 2xzγxz + 2yzγyz) γr𝜃 = 1 rρ(x2zγ xx + y2zγ yy zρ2γ zz + 2xyzγxy + x(z2 ρ2)γ xz + y(z2 ρ2)γ yz) γrϕ = 1 r(xyγxx + xyγyy + (x2 y2)γ xy yzγxz + xzγyz) γ𝜃𝜃 = 1 ρ2(x2z2γ xx + 2xyz2γ xy 2xzρ2γ xz + y2z2γ yy 2yzρ2γ yz + ρ4γ zz) γ𝜃ϕ = 1 ρ(xyzγxx + (x2 y2)zγ xy + ρ2yγ xz + xyzγyy ρ2xγ yz) γϕϕ = y2γ xx 2xyγxy + x2γ yy

or,

γrr = sin2𝜃cos2ϕγ xx + sin2𝜃sin2ϕγ yy + cos2𝜃γ zz + 2sin2𝜃cosϕsinϕγ xy + 2sin𝜃cos𝜃cosϕγxz +2sin𝜃cos𝜃sinϕγyz γr𝜃 = r(sin𝜃cos𝜃cos2ϕγ xx + 2 sin𝜃cos𝜃sinϕcosϕγxy + (cos2𝜃 sin2𝜃)cosϕγ xz + sin𝜃cos𝜃sin2ϕγ yy +(cos2𝜃 sin2𝜃)sinϕγ yz sin𝜃cos𝜃γzz) γrϕ = rsin𝜃(sin𝜃sinϕcosϕγxx sin𝜃(sin2ϕ cos2ϕ)γ xy cos𝜃sinϕγxz + sin𝜃sinϕcosϕγyy +cos𝜃cosϕγyz) γ𝜃𝜃 = r2(cos2𝜃cos2ϕγ xx + 2cos2𝜃sinϕcosϕγ xy 2sin𝜃cos𝜃cosϕγxz + cos2𝜃sin2ϕγ yy 2sin𝜃cos𝜃sinϕγyz + sin2𝜃γ zz) γ𝜃ϕ = r2 sin𝜃(cos𝜃sinϕcosϕγ xx cos𝜃(sin2ϕ cos2ϕ)γ xy + sin𝜃sinϕγxz + cos𝜃sinϕcosϕγyy sin𝜃cosϕγyz) γϕϕ = r2 sin2𝜃(sin2ϕγ xx 2sinϕcosϕγxy + cos2ϕγ yy)

We also need the transformation for the radial derivative of the metric components:

γrr,η = sin2𝜃cos2ϕγ xx,η + sin2𝜃sin2ϕγ yy,η + cos2𝜃γ zz,η + 2sin2𝜃cosϕsinϕγ xy,η +2sin𝜃cos𝜃cosϕγxz,η + 2sin𝜃cos𝜃sinϕγyz,η γr𝜃,η = 1 rγr𝜃 + r(sin𝜃cos𝜃cos2ϕγ xx,η + sin𝜃cos𝜃sinϕcosϕγxy,η + (cos2𝜃 sin2𝜃)cosϕγ xz,η +sin𝜃cos𝜃sin2ϕγ yy,η + (cos2𝜃 sin2𝜃)sinϕγ yz,η sin𝜃cos𝜃γzz,η) γrϕ,η = 1 rγrϕ + rsin𝜃(sin𝜃sinϕcosϕγxx,η sin𝜃(sin2ϕ cos2ϕ)γ xy,η cos𝜃sinϕγxz,η +sin𝜃sinϕcosϕγyy,η + cos𝜃cosϕγyz,η) γ𝜃𝜃,η = 2 rγ𝜃𝜃 + r2(cos2𝜃cos2ϕγ xx,η + 2cos2𝜃sinϕcosϕγ xy,η 2sin𝜃cos𝜃cosϕγxz,η +cos2𝜃sin2ϕγ yy,η 2sin𝜃cos𝜃sinϕγyz,η + sin2𝜃γ zz,η) γ𝜃ϕ,η = 2 rγ𝜃ϕ + r2 sin𝜃(cos𝜃sinϕcosϕγ xx,η cos𝜃(sin2ϕ cos2ϕ)γ xy,η + sin𝜃sinϕγxz,η +cos𝜃sinϕcosϕγyy,η sin𝜃cosϕγyz,η) γϕϕ,η = 2 rγϕϕ + r2 sin2𝜃(sin2ϕγ xx,η 2sinϕcosϕγxy,η + cos2ϕγ yy,η)

8 Appendix: Integrations Over the 2-Spheres

This is done by using Simpson’s rule twice. Once in each coordinate direction. Simpson’s rule is

x1x2 f(x)dx = h 3[f1 + 4f2 + 2f3 + 4f4 + + 2fN2 + 4fN1 + fN] + O(1N4) (32)

N must be an odd number.

References

[1]   Abrahams A.M. & Cook G.B. “Collisions of boosted black holes: Perturbation theory predictions of gravitational radiation” Phys. Rev. D 50 R2364-R2367 (1994).

[2]   Abrahams A.M., Shapiro S.L. & Teukolsky S.A. “Calculation of gravitational wave forms from black hole collisions and disk collapse: Applying perturbation theory to numerical spacetimes” Phys. Rev. D. 51 4295 (1995).

[3]   Abrahams A.M. & Price R.H. “Applying black hole perturbation theory to numerically generated spacetimes” Phys. Rev. D. 53 1963 (1996).

[4]   Abrahams A.M. & Price R.H. “Black-hole collisions from Brill-Lindquist initial data: Predictions of perturbation theory” Phys. Rev. D. 53 1972 (1996).

[5]   Abramowitz, M. & Stegun A. “Pocket Book of Mathematical Functions (Abridged Handbook of Mathematical Functions”, Verlag Harri Deutsch (1984).

[6]   Andrade Z., & Price R.H. “Head-on collisions of unequal mass black holes: Close-limit predictions”, preprint (1996).

[7]   Anninos P., Price R.H., Pullin J., Seidel E., and Suen W-M. “Head-on collision of two black holes: Comparison of different approaches” Phys. Rev. D. 52 4462 (1995).

[8]   Arfken, G. “Mathematical Methods for Physicists”, Academic Press (1985).

[9]   Baker J., Abrahams A., Anninos P., Brant S., Price R., Pullin J. & Seidel E. “The collision of boosted black holes” (preprint) (1996).

[10]   Baker J. & Li C.B. “The two-phase approximation for black hole collisions: Is it robust” preprint (gr-qc/9701035), (1997).

[11]   Brandt S.R. & Seidel E. “The evolution of distorted rotating black holes III: Initial data” (preprint) (1996).

[12]   Cunningham C.T., Price R.H., Moncrief V., “Radiation from collapsing relativistic stars. I. Linearized Odd-Parity Radiation” Ap. J. 224 543-667 (1978).

[13]   Cunningham C.T., Price R.H., Moncrief V., “Radiation from collapsing relativistic stars. I. Linearized Even-Parity Radiation” Ap. J. 230 870-892 (1979).

[14]   Landau L.D. & Lifschitz E.M., “The Classical Theory of Fields” (4th Edition), Pergamon Press (1980).

[15]   Mathews J. “”, J. Soc. Ind. Appl. Math. 10 768 (1962).

[16]   Moncrief V. “Gravitational perturbations of spherically symmetric systems. I. The exterior problem” Annals of Physics 88 323-342 (1974).

[17]   Press W.H., Flannery B.P., Teukolsky S.A., & Vetterling W.T., “Numerical Recipes, The Art of Scientific Computing” Cambridge University Press (1989).

[18]   Price R.H. & Pullin J. “Colliding black holes: The close limit”, Phys. Rev. Lett. 72 3297-3300 (1994).

[19]   Regge T., & Wheeler J.A. “Stability of a Schwarzschild Singularity”, Phys. Rev. D 108 1063 (1957).

[20]   Seidel E. Phys Rev D. 42 1884 (1990).

[21]   Thorne K.S., “Multipole expansions of gravitational radiation”, Rev. Mod. Phys. 52 299 (1980).

[22]   Vishveshwara C.V., “Stability of the Schwarzschild metric”, Phys. Rev. D. 1 2870, (1970).

[23]   Zerilli F.J., “Tensor harmonics in canonical form for gravitational radiation and other applications”, J. Math. Phys. 11 2203, (1970).

[24]   Zerilli F.J., “Gravitational field of a particle falling in a Schwarzschild geometry analysed in tensor harmonics”, Phys. Rev. D. 2 2141, (1970).

9 Parameters




all_modes
Scope: private  BOOLEAN



Description: Extract: all l,m modes up to l



  Default: yes






cauchy
Scope: private  BOOLEAN



Description: Do Cauchy data extraction at given timestep



  Default: no






cauchy_dr
Scope: private  REAL



Description: Gridspacing for Cauchy data extraction



Range   Default: 0.2
*:*






cauchy_r1
Scope: private  REAL



Description: First radius for Cauchy data extraction



Range   Default: 1.0
*:*






cauchy_timestep
Scope: private  INT



Description: Timestep for Cauchy data extraction



Range   Default: (none)
0:*






detector1
Scope: private  REAL



Description: Coordinate radius of detector 1



Range   Default: 5.0
0:*






detector2
Scope: private  REAL



Description: Coordinate radius of detector 2



Range   Default: 5.0
0:*






detector3
Scope: private  REAL



Description: Coordinate radius of detector 3



Range   Default: 5.0
0:*






detector4
Scope: private  REAL



Description: Coordinate radius of detector 4



Range   Default: 5.0
0:*






detector5
Scope: private  REAL



Description: Coordinate radius of detector 5



Range   Default: 5.0
0:*






detector6
Scope: private  REAL



Description: Coordinate radius of detector 6



Range   Default: 5.0
0:*






detector7
Scope: private  REAL



Description: Coordinate radius of detector 7



Range   Default: 5.0
0:*






detector8
Scope: private  REAL



Description: Coordinate radius of detector 8



Range   Default: 5.0
0:*






detector9
Scope: private  REAL



Description: Coordinate radius of detector 9



Range   Default: 5.0
0:*






do_momentum
Scope: private  BOOLEAN



Description: Calculate momentum at extraction radii



  Default: no






do_spin
Scope: private  BOOLEAN



Description: Calculate spin at extraction radii



  Default: no






doadmmass
Scope: private  BOOLEAN



Description: Calculate ADM mass at extraction radii



  Default: no






interpolation_operator
Scope: private  STRING



Description: Interpolation operator to use (check LocalInterp)



Range   Default: uniform cartesian
.+






interpolation_order
Scope: private  INT



Description: Order for interpolation



Range   Default: 1
1:4
Choose between first and forth order interpolation






itout
Scope: private  INT



Description: How often to extract, in iterations



Range   Default: 1
0:*






l_mode
Scope: private  INT



Description: l mode



Range   Default: 2
0:*






m_mode
Scope: private  INT



Description: m mode (ignore if extracting all modes



Range   Default: (none)
0:*






np
Scope: private  INT



Description: Number of phi divisions



Range   Default: 100
0:*






nt
Scope: private  INT



Description: Number of theta divisions



Range   Default: 100
0:*






num_detectors
Scope: private  INT



Description: Number of detectors



Range   Default: (none)
0:*






origin_x
Scope: private  REAL



Description: x-origin to extract about



Range   Default: 0.0
*:*






origin_y
Scope: private  REAL



Description: y-origin to extract about



Range   Default: 0.0
*:*






origin_z
Scope: private  REAL



Description: z-origin to extract about



Range   Default: 0.0
*:*






timecoord
Scope: private  KEYWORD



Description: Which time coordinate to use



Range   Default: both
proper
coordinate
both






verbose
Scope: private  BOOLEAN



Description: Say what is happening



  Default: no






out_dir
Scope: shared from IO STRING



10 Interfaces

General

Implements:

extract

Inherits:

grid

admbase

staticconformal

io

Grid Variables

10.0.1 PRIVATE GROUPS




  Group Names    Variable Names    Details   




temps   compact0
temp3d   dimensions3
g00   distributionDEFAULT
  group typeGF
  timelevels1
 variable typeREAL




11 Schedule

This section lists all the variables which are assigned storage by thorn EinsteinAnalysis/Extract. 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

  extract_paramcheck

  check parameters

 

 Language:c
 Options: global
 Type: function

CCTK_POSTSTEP

  extract

  extract waveforms

 

 Language:fortran
 Storage: temps
 Type: function