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GRTensor.m

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  • GRTensor.m 69.95 KiB
    (* ::Package:: *)
    
    (************************************************************************)
    (* This file was generated automatically by the Mathematica front end.  *)
    (* It contains Initialization cells from a Notebook file, which         *)
    (* typically will have the same name as this file except ending in      *)
    (* ".nb" instead of ".m".                                               *)
    (*                                                                      *)
    (* This file is intended to be loaded into the Mathematica kernel using *)
    (* the package loading commands Get or Needs.  Doing so is equivalent   *)
    (* to using the Evaluate Initialization Cells menu command in the front *)
    (* end.                                                                 *)
    (*                                                                      *)
    (* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)
    (* automatically each time the parent Notebook file is saved in the     *)
    (* Mathematica front end.  Any changes you make to this file will be    *)
    (* overwritten.                                                         *)
    (************************************************************************)
    
    
    
    
    (* Probably not all the extra packages are really needed *)
    BeginPackage["GRTensor`"];
    
    
    MetDet::usage="MetDet[g_]. Compute the determinant of the metric";
    InverseMetric::usage="InverseMetric[g_]. Compute the inverse of the metric";
    
    
    ChristoffelSymbol::usage="ChristoffelSymbol[coords_,g_,pert_:0]. Compute Christoffel symbols.  Default for perturbation variabel pert is 0.";
    WeylTensor::usage="WeylTensor[coords_,g_,pert_:0]. Compute Weyl tensor following the convention of Misner et al., that is, [S2] = 1, [S3] = 1. Default for perturbation variabel pert is 0. ";
    RiemannTensor::usage="RiemannTensor[coords_,g_,pert_:0]. Compute Riemann tensor following the convention of Misner et al., that is, [S2] = 1, [S3] = 1 .Default for perturbation variabel pert is 0. ";
    RicciTensor::usage="RicciTensor[coords_,g_,pert_:0]. Compute Riemann tensor following the convention of Misner et al., that is, [S2] = 1, [S3] = 1. Default for perturbation variabel pert is 0. ";
    RicciScalar::usage="RicciScalar[coords_,g_,pert_:0]. Compute RicciScalar scalar. Default for perturbation variabel pert is 0. ";
    KrScalar::usage="KrScalar[coords_,g_]. Compute Kretschmann scalar";
    WeylTrace::usage"WeylTrace[coords_,g_]: Compute Weyl Tensor trace";
    Einstein::usage="Einstein[coords_,g_,\[Epsilon]p:]. Compute Einstein tensor following the convention of Misner et al., that is, [S2] = 1, [S3] = 1 with perturbation index \[Epsilon]p";
    ETensor::usage="ETensor[coords_,g_,\[Epsilon]p_]. Compute the energy momentum tensor  with perturbation index \[Epsilon]p.";
    
    
    DAlembert::usage="DAlembert[coords_,g_,func_]. Compute D'Alembert operator for func[coords]";
    CovDer::usage="CovDer[coords_,metric_,tensor_,comps_]. Compute the covariant derivative (default covariant version) for scalar and 1-2 forms. The components are given in a list as: {a},{a,b},{a,b,c}";
    NonZeroChristoffel::usage="NonZeroChristoffel[\[CapitalGamma]]. Show the nonzero Christoffel components.";
    NonZeroMetricComp::usage="NonZeroMetricComp[g]. Show the nonzero metric components.";
    NonZeroTensorComp::usage="NonZeroTensorComp[T]. Show the nonzero Tensor components. It works with any symmetric m xmxmxmx... tensor";
    LeviCivitaTensorCurv::usage="LeviCivitaTensorCurv[coords_,g_]. Compute the Levi-Civita antisymmetric tensor for curvilinear coordinates. For cartesian xx recovers the usual \[Epsilon]_(abc).";
    CheckTetrad::usage="[gab_,nullv_]. Check whether the 4 null tetrad vectors satisfy orthonormality conditions.";
    
    
    EinsteinfR::usage="EinsteinfR[coords_,g_,fR_]. Compute fR Einstein equations following the convention of Misner et al., that is, [S2] = 1, [S3] = 1 ";
    EinsteinST::usage="EinsteinST[coords_,g_,v\[Phi]_]. Compute scalar-tensor Einstein equations following the convention of Misner et al., that is, [S2] = 1, [S3] = 1 ";
    STensorT\[Psi]::usage="STensorT\[Psi][coords_,g_,v\[Phi]_]. Compute scalar-tensor Energy momentum tensor following the convention of Misner et al., that is, [S2] = 1, [S3] = 1 ";
    TeffFR::usage="TeffFR[coords_,g_,fR_]. Compute fR Teff tensor such Gab=8\[Pi]/f'[R](Tab + Teff) following the convention of Misner et al., that is, [S2] = 1, [S3] = 1";
    TeffST::usage="TeffST[coords_,g_,{V\[CurlyPhi],\[CurlyPhi]}]. Compute ST-EF/JF Teff tensor such Gab=8\[Pi] (Tab + Teff) following the convention of Misner et al., that is, [S2] = 1, [S3] = 1. Allowed options for the Frame are Einstein, Jordan";
    FRTOV::usage="FRTOV[coords_,g_,fR_,vars_]. Compute fR TOV eqs such Gab=8\[Pi]/f'[R](Tab + Teff) following the convention of Misner et al., that is, [S2] = 1, [S3] = 1";
    STTOV::usage="STTOV[coords_,g_,{V\[CurlyPhi]_,var\[CurlyPhi]_},vars_]. Compute ST-EF/JF TOV eqs such Gab=8\[Pi](Tab + Teff) following the convention of Misner et al., that is, [S2] = 1, [S3] = 1";
    fR2Pot::usage="fR2UJF[fR_]. From fR model to the ST potential U(\[Phi])-V(\[Phi])";
    CurlCurvilinear::usage"CurlCurvilinear[xx,g,vec]. It computes the curl tensor in curvilinear coordinates";
    ElectricTensor3p1Dev::usage="ElectricTensor3p1Dev[xx_,g_,Kt_,pert_:0,OptionsPattern[]]";
    MagneticTensor3p1Dev::usage="MagneticTensor3p1Dev[xx_,g_,Kt_,pert_:0,OptionsPattern[]]"
    
    
    EoSCallParsBSks::usage="EoSCallParsBSks[model_]: Parameters for BSK1-3 EOS for the matter density.";
    EoSCallParsSly::usage="EoSCallParsSly[model_]: Parameters for SLy1 EOS for the matter density.";
    EoSBSks::usage="EoSBSks[model_]: Analytic EOS for BSK1-3for BSK1-3 EOS for the matter density.";
    EoSSly::usage="EoSSly[model_]:  Analytic EOS for SLy1 EOS for the matter density.";
    SlyInner::usage="";
    SlyLCore::usage="";
    SlyLCoreAll::usage="";