g=DiagonalMatrix[{-1, (((a[t])^2)/(1-k (r^2))), ((a[t])^2)(r^2), ((a[t])^2)(r^2)Sin[θ]^2}]

g//MatrixForm

gInv=Inverse[g]

gInv//MatrixForm

der[λ_]:=Which[λ==0,D[#,t],λ==1,D[#,r],λ==2,D[#,θ],λ==3,D[#,ϕ]]&

der[2]@f[t,r,θ,ϕ]

christoffel[μ_,ν_,λ_]:=(1/2)(∑_({κ,0,3}))gInv[[κ+1,λ+1]]*(der[μ]@g[[ν+1,κ+1]]+der[ν]@g[[μ+1,κ+1]]-der[κ]@g[[μ+1,ν+1]])

helplist1=Tuples[{0,1,2,3},3]

length=Length[Tuples[{0,1,2,3},3]];

helplist2=christoffel[#[[1]],#[[2]],#[[3]]]&/@Tuples[{0,1,2,3},3]

christoffelList=Table[{helplist1[[i]],helplist2[[i]]},{i,1,length}];

christoffelList//MatrixForm

nonZeroChristoffelList=Select[christoffelList,Not[#[[2]]===0]&];

nonZeroChristoffelList//MatrixForm

replaceIndex[λ_]:=Which[λ==0,"t",λ==1,"r",λ==2,"θ",λ==3,"ϕ"]

Print[
Subsuperscript[
"Γ",
replaceIndex[#[[1,1]]]<>replaceIndex[#[[1,2]]], (* subscript *)
replaceIndex[#[[1,3]]] (* superscript *)
],"=" ,
#[[2]] (* value *)
]&/@nonZeroChristoffelList;