Quit

<<xAct`xCoba`

$PrePrint=ScreenDollarIndices;

$DefInfoQ=False;
$UndefInfoQ=False;

<<xAct`ShowTime1`;

$ShowTimeThreshold=0.3;

DefManifold[AdS,4,IndexRange[a,h]];

DefChart[Global,AdS,{0,1,2,3},{t[],r[],θ[],ϕ[]}];

DefConstantSymbol[Mass,PrintAs->"M"];

DefConstantSymbol[Omega,PrintAs->"ω"];

$Assumptions=Mass>0 && r[]> 0 && r<π/2 && Element[Omega,Reals];

metric = CTensor[DiagonalMatrix[{-((Sec[r[]])^2),((Sec[r[]])^2),((Tan[r[]])^2),((Tan[r[]])^2)((Sin[θ[]])^2)}],{-Global,-Global}];

SetCMetric[metric,Global];

MetricCompute[metric,Global,All,CVSimplify-> Simplify];

CD = CovDOfMetric[metric]

Chr = Christoffel[CD,PDGlobal]

xAct`xCoba`Private`moveto[n_,n_]:={1}

DefConstantSymbol[l];

DefConstantSymbol[m];

metric2 = CTensor[DiagonalMatrix[{0,0,metric[{1,Global},{1,Global}],metric[{2,Global},{2,Global}]}],{Global,Global}]

metric2[{a,Global},{b,Global}]CD[{-a,-Global}]@CD[{-b,-Global}]@SphericalHarmonicY[l,m,θ[],ϕ[]]

Simplify[%]