Needs["grt`","/home/pascal/projects/grtensorm/grt.m"]

?grt

?grt`*

coord1={t,x,y,z};
metric1={{1 (1-2 ϵ ψ[t,x,y,z]),0,0,0},{0,-(1+2 ϵ Φ[t,x,y,z])a[t]^2,0,0},{0,0,-(1+2ϵ Φ[t,x,y,z]) a[t]^2,0},{0,0,0,-(1+2ϵ Φ[t,x,y,z])a[t]^2}};

LoadMetric[coord1,metric1]

Coefficient[Series[grt`Private`EinsteinTensor,{ϵ,0,1}],ϵ,1]

ShowΓ

ShowCurvatureTensor

ShowRicciTensor

ShowEinsteinTensor

RicciScalar

Quabla[f[t]]

tanmnayCoords={t,r,θ,ϕ};
tanmay={{((a[t])^2) f[t,r],0,0,0},{0,-((a[t])^2)h1[t,r],0,0},{0,0,((a[t])^2)h2[t,r] (r^2),0},{0,0,0,((a[t])^(2 ))h2[t,r] (r^2)((Sin[θ])^(2 ))}};

LoadMetric[tanmnayCoords,tanmay]

RicciScalar

Table[G[(SubMinus[a]),(SubMinus[b])],{a,1,4},{b,1,4}]

G[(SubMinus[1]),(SubMinus[1])]

f[x]=(x^2)

DownValues[f]