xx ScalarBase

ScalarBase

Miguel Zilhxo <mzilhao@ua.pt>

July 1 2023

Abstract

ScalarBase adds an interface to include scalar fields within the Einstein Toolkit framework. In the same spirit as ADMBase and HydroBase, this thorn merely stores the variables used in typical scalar field evolutions as well as commonly needed parameters. This thorn was primarily designed to work with the ScalarEvolve thorn, but in principle any other scalar field evolution code could be used.

1 ScalarBase

This thorn defines a set of variables and parameters commonly needed to evolve (complex) scalar fields, potentially coupled to the Einstein field equations. Currently it defines the gridfunctions phi1 and phi2, as well as their “conjugated momenta” Kphi1 and Kphi2. It also declares the parameter mu, the scalar field mass.

This thorn is designed to interface with the evolution thorn ScalarEvolve, but any other scalar evolution code should also work. Within ScalarEvolve, the variables phi1 and phi2 represent the real and imaginary parts of some complex scalar field , satisfying the Einstein-Klein-Gordon system

where is the mass parameter (denoted by mu in param.ccl) and

2 Obtaining This Thorn

This thorn is included in the Einstein Toolkit and can also be obtained through the Canuda numerical relativity libraryx[1].

References

[1]xxxH.xWitek, M.xZilhao, G.xBozzola, C.-H.xCheng, A.xDima, M.xElley, G.xFicarra, T.xIkeda, R.xLuna, C.xRichards, N.xSanchis-Gual, H.xOkadaxdaxSilva. “Canuda: a public numerical relativity library to probe fundamental physics,” Zenodo (2023) doi: 10.5281/zenodo.3565474

3 Parameters

11 ampef 10 Scope: restricted01 REAL

11 Description: amplitude of external forcing

11 Range 10 01 Default: 1.0
11 *:*  10 Any value possible

11 epsxr  10 Scope: restricted01  REAL

11 Description: of value if rr approaches zero in densities computation

11 Range 10 01 Default: 1.0d-06
11 0:*  10 any small positive value possible

11

11 evolutionxmethod10 Scope: restricted01  KEYWORD

11 Description: scalar variables evolution method

11 Range 10 01 Default: none
11 none  10 scalar variables are not evolved

11

11 forcingxswitch 10 Scope: restricted01  BOOLEAN

11 Description: add external forcing to the rhs of Klein-Gordon

11                 10                01  Default: no

11

11 initialxscalar  10 Scope: restricted01  KEYWORD

11 Description: initial data for scalar variables

11 Range 10 01 Default: none
11 none  10 scalar variables are not initialized

11

11 kphi1x0  10 Scope: restricted01  REAL

11 Description: asymptotic value for Kphi1

11  Range  10                01  Default: (none)

11 *:*  10

11

11 kphi2x0  10 Scope: restricted01  REAL

11 Description: asymptotic value for Kphi2

11  Range  10                01  Default: (none)

11 *:*  10

11

11 lef  10 Scope: restricted01  INT

11 Description:

11 Range 10 01 Default: (none)
11 0:2  10 angular multipoles implemented are l = m = 0,1,2

11

11 mef  10 Scope: restricted01  INT

11 Description:

11 Range 10 01 Default: (none)
11 0:2  10 angular multipoles implemented are l = m = 0,1,2

11

11 mu  10 Scope: restricted01  REAL

11 Description: mass of the scalar fields

11 Range 10 01 Default: (none)
11 0:*  10 any non-negative number

11 nxkphi1  10 Scope: restricted01  INT

11 Description: n power of outgoing boundary rn̂ fall off rate for Kphi1

11 Range 10 01 Default: 2
11 0:4  10 ??

11

11 nxkphi2  10 Scope: restricted01  INT

11 Description: n power of outgoing boundary rn̂ fall off rate for Kphi2

11 Range 10 01 Default: 2
11 0:4  10 ??

11

11 nxphi1  10 Scope: restricted01  INT

11 Description: n power of outgoing boundary rn̂ fall off rate for phi1

11 Range 10 01 Default: 1
11 0:4  10 ??

11

11 nxphi2  10 Scope: restricted01  INT

11 Description: n power of outgoing boundary rn̂ fall off rate for phi2

11 Range 10 01 Default: 1
11 0:4  10 ??

11

11 omegaef  10 Scope: restricted01  REAL

11 Description: oscillation frequency of external forcing

11 Range 10 01 Default: 0.0
11 0:*  10 Any positive value

11

11 phi1x0  10 Scope: restricted01  REAL

11 Description: asymptotic value for phi1

11  Range  10                01  Default: (none)

11 *:*  10

11

11 phi2x0  10 Scope: restricted01  REAL

11 Description: asymptotic value for phi2

11  Range  10                01  Default: (none)

11 *:*  10

11

11 ref  10 Scope: restricted01  REAL

11 Description: peak position of external forcing

11 Range 10 01 Default: 10.0
11 0:*  10 Any positive value

11

11 vxlambda  10 Scope: restricted01  REAL

11 Description: interaction term in the potential

11  Range  10                01  Default: (none)

11 *:*  10

11 widthef  10 Scope: restricted01  REAL

11 Description: width of external forcing

11 Range 10 01 Default: 10.0
11 0:*  10 Any positive value

11

4 Interfaces

General Implements: scalarbase

Inherits: grid

Grid Variables

4.0.1 PUBLIC GROUPS

11 x Group Names x 10 x Variable Names x01 Details x 11 x
11  phi  10                    01  compact 11 0
11                    10  phi1  01 description 11 scalar fields
11                    10  phi2  01 dimensions 11 3
11                    10                    01 distribution 11 DEFAULT
11                    10                    01 group type 11 GF
11                    10                    01  tags 11 tensortypealias=”Scalar” tensorweight=0
11                    10                    01 timelevels 11 3
11                    10                    01 variable type 11 REAL
11  kphi  10                    01  compact 11 0
11                    10  Kphi1  01 description 11 their conjugated momenta
11                    10  Kphi2  01 dimensions 11 3
11                    10                    01 distribution 11 DEFAULT
11                    10                    01 group type 11 GF
11                    10                    01  tags 11 tensortypealias=”Scalar” tensorweight=0
11                    10                    01 timelevels 11 3
11                    10                    01 variable type 11 REAL
11  fext  10                    01  compact 11 0
11                    10  Fext1  01 description 11 scalar field external forcing function
11                    10  Fext2  01 dimensions 11 3
11                    10                    01 distribution 11 DEFAULT
11                    10                    01 group type 11 GF
11                    10                    01  tags 11 tensortypealias=”Scalar” tensorweight=0
11                    10                    01 timelevels 11 3
11                    10                    01 variable type 11 REAL

11

5 Schedule This section lists all the variables which are assigned storage by thorn Scalar/ScalarBase. 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 x

11 Always:  11 Conditional:
11 phi[3] Kphi[3] 11 Fext[3]

11 x  11 x

11

Scheduled Functions

CCTKxWRAGH x scalarbasexsymmetries x register symmetries of the grid functions x

11 x 11 Language: 11 fortran
11 x 11 Options: 11 global
11 x 11 Type:  11 function

11

MoLxStep (conditional) x scalarxrhsxforce x writes external force grid function x

11 x 11 Before: 11 molxcalcrhs
11 x 11 Language: 11 fortran
11 x 11 Options: 11 local
11 x 11 Type:  11 function