Trying to calculate tidal tensor for Kerr-Newman

[Flo Flo]

Hello ! 

I don't know anything about mathematical or xAct, I just want to calculate the tidal tensor for Kerr-Newman geometry for a ZAMO observer (but with r and theta fixed).

After hours with AIs and many errors and many try it still doesn't work and I desesperate...

I've Wolfram 15.0.0 and xAct 1.3.0, my code is :

Needs["xAct`xTensor`"];
Needs["xAct`xCoba`"];

DefManifold[M4, 4, {a,b,c,d}];
DefCoordinates[{tt, rr, thh, phh}, M4];

DefMetric[-1, g[-a,-b], CD];
DefConstantSymbol[{M, aPar, Q}];

Sigma = rr^2 + aPar^2 Cos[thh]^2;
Delta = rr^2 - 2 M rr + aPar^2 + Q^2;

gBL = {
 {-(1 - (2 M rr - Q^2)/Sigma), 0, 0,
  -((2 M rr - Q^2) aPar Sin[thh]^2)/Sigma},
 {0, Sigma/Delta, 0, 0},
 {0, 0, Sigma, 0},
 {-((2 M rr - Q^2) aPar Sin[thh]^2)/Sigma, 0, 0,
  Sin[thh]^2 (rr^2 + aPar^2 +
    (2 M rr - Q^2) aPar^2 Sin[thh]^2/Sigma)}
};

ComponentValue[g[-a,-b], gBL];

Rcomp = Table[
  ComponentValue[RiemannCD[-a,-b,-c,-d], {a->α, b->β, c->γ, d->δ}],  {α,1,4},{β,1,4},{γ,1,4},{δ,1,4}];

A     = (rr^2 + aPar^2)^2 - aPar^2 Delta Sin[thh]^2;
omega = (2 M rr - Q^2) aPar / A;
alpha = Sqrt[Delta Sigma / A];

e0   = {1/alpha, 0, 0, omega/alpha};
er   = {0, Sqrt[Delta/Sigma], 0, 0};
eth  = {0, 0, 1/Sqrt[Sigma], 0};
ephi = {0, 0, 0, Sqrt[Sigma]/(Sqrt[A] Sin[thh])};

spatialTetrad = {er, eth, ephi};

TidalTensor =
 Table[  Sum[
   Rcomp[[α, β, γ, δ]] *
   e0[[α]] * spatialTetrad[[i]][[β]] *
   e0[[γ]] * spatialTetrad[[j]][[δ]],
   {α,1,4},{β,1,4},{γ,1,4},{δ,1,4}
  ] // Simplify,
  {i,1,3},{j,1,3}
 ];

Err      = TidalTensor[[1,1]];
Erth     = TidalTensor[[1,2]];
Erphi    = TidalTensor[[1,3]];
Ethth    = TidalTensor[[2,2]];
Ethphi   = TidalTensor[[2,3]];
Ephiphi  = TidalTensor[[3,3]];

Can someone please help me ?

Thank you