evaluation of weff

code/GRTensor.m

@@ -56,6 +56,7 @@ TeffST::usage="TeffST[coords_,g_,{V\[CurlyPhi],\[CurlyPhi]}]. Compute ST-EF/JF T
 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])";
+fR2\[Phi]::usage="fR2\[Phi][fR_]. From fR model to the ST potential";
 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[]]"
@@ -77,6 +78,9 @@ EoSPol\[Epsilon]::usage="EoSPol\[Epsilon][model_]. NS EOS for a non-relativistic
 From\[Rho]To\[Epsilon]Fits::usage"From\[Rho]To\[Epsilon]Fits[eos_]. NS EOS of JRead(arxiv:0812.2163) for the energy density.";
 
 
+\[Omega]eff::usage="\[Omega]eff[fR_,OptionsPattern]. It computes the effective equation of state given the fR model. It also provides the same for scalar tensor theory in the JF.";
+
+
 ShootingNStars::usage="ShootingNStars[eqs_,eqsRg_,rvar_,vars_,shtdInd_,varshtdRg_]. Shooting function of the index var shtdInd for a set of eqs integrated in eqsRg on the variables vars ;";
 BracketingSTNStars::usage="BracketingSTNStars[eqs_,eqsRg_,rvar_,vars_,shtdInd_,varshtdRg_]. Shooting function of the index var shtdInd for a set of eqs integrated in eqsRg on the variables vars ;";
 
@@ -534,6 +538,33 @@ res=Table[If[NumericQ[pert],riemann[[i,k,l,m]]+1/(n-2)(ricciT[[i,m]]g[[k,l]]-ric
 simpl@res];
 
 
+Options[\[Omega]eff]={"ST"->False,"SimplifyFunction"->Identity};
+\[Omega]eff[fR_,OptionsPattern[]]:=Block[{dR,dR2,expr,Global`x,f,fRterm1,fRc,fRterm2,dalem,dfRc,dfRc2,dfRc3,Global`H,Hc,Global`R,Rc,Rc\[Phi],res,riscal,riscalvars,simpl,st,Global`t,tc,Global`\[Phi],\[Phi]c},
+st=OptionValue["ST"];
+simpl=OptionValue["SimplifyFunction"];
+
+Rc=Global`R;
+tc=Global`t;
+Hc=Global`H;
+\[Phi]c=Global`\[Phi];
+If[st,Rc\[Phi]=fR2\[Phi][fR]/.\[Phi]c->\[Phi]c[t]];
+
+dR=D[Rc[tc],tc];
+dR2=D[Rc[tc],{tc,2}];
+fRc=fR/.Global`R->Rc[tc];
+dfRc=D[fRc,Rc[tc]];
+dfRc2=D[fRc,{Rc[tc],2}];
+dfRc3=D[fRc,{Rc[tc],3}];
+
+If[fRc==Rc[tc],Return[-1]];
+
+res=(dR^2 dfRc3 + 2Hc[tc]dfRc2 dR + dR2 dfRc2 + 1/2(fRc-Rc[tc]dfRc))/((Rc[tc]dfRc-fRc)/2-3Hc[tc]dR dfRc2);
+If[st,res=Block[{R},Rc[t_]:=Evaluate@Rc\[Phi];res]];
+
+simpl@res
+];
+
+
 Options[EinsteinfR]={{"Metric"->True},Join[Options[ChristoffelSymbol]]};
 EinsteinfR[xx_,g_,fR_,OptionsPattern[]]:=Block[{res,fRterm1,fRterm2,dalem,Global`R,riscal,riscalvars,simpl,Rc,fRc,dfRc,covterm1,covterm2,metric},
 
@@ -778,6 +809,19 @@ fun
 ];
 
 
+fR2\[Phi][fR_,\[Phi]\[CurlyPhi]_:1]:=Block[{dfRc,fRc,fun,Rc,uc,Global`R,Global`\[Phi],\[Phi]c,Rc\[Phi]},
+
+Rc=Global`R;
+\[Phi]c=Global`\[Phi];
+fRc=fR/.Global`R->Rc;
+dfRc=D[fRc,Rc];
+
+Rc\[Phi]=(Rc/.Solve[\[Phi]c==dfRc,Rc]);
+$Assumptions = _ \[Element] Reals;
+Rc\[Phi][[1]]
+];
+
+
 Pot2fR[V\[CurlyPhi]_,\[Phi]\[CurlyPhi]_]:=Block[{dfRc,fRc,fun,Rc,uc,Global`R,Global`\[Phi],Global`\[CurlyPhi],\[Phi]c,Rc\[Phi],\[CurlyPhi]c},