PacletInstall["BowenPing`STensor`"]
In[]:=
Needs["BowenPing`STensor`"]
In[]:=
g=CreateTensor"g",{t,r,θ,ϕ},DiagonalMatrix-1-
2M
r
,
-1
1-
2M
r
,
2
r
,
2
r
2
Sin[θ]
,IsMetric->True;
In[]:=
Rdown=Head[g["ce"]RiemannTensor[g]["e","abd"]]
Out[]=
STensor
Symbol: g Riemann(g)
Rank: {0,4}

In[]:=
Rup=Head[RiemannTensor[g]["a","efg"]Inverse[g]["be"]Inverse[g]["cf"]Inverse[g]["dg"]]
Out[]=
STensor
Symbol: g g g Riemann(g)
Rank: {4,0}

In[]:=
Rup["abcd"]Rdown["abcd"]
Out[]=
-
24
2
M
6
r