Hello, I'm doing the calculation of the Tide tensor, and although the expression is correct at the end, the sign of the expression is incorrect. That makes me think that the problem is in some configuration of the simmetries of the Riemann tensor. The problem might be a result of a poor use of the system by me. I'll put the code for Reissner-Nordström spacetimes as an example
{r,t,\phi,\theta}::Coordinate; {\mu,\nu,\rho,\sigma,\lambda,\kappa,\chi,\gamma, \tau, \beta, a, b}::Indices(values={t,r,\phi,\theta}, position=fixed); \partial{#}::PartialDerivative; g_{\mu\nu}::Metric. g^{\mu\nu}::InverseMetric. R^{\rho}_{\sigma\mu\nu}::RiemannTensor.
`ss:= { g{t t} = 1-2*M/r + q2/r2,
g{r r} = -1/(1-2*M/r + q2/r2),
g{\theta\theta} = -r**2,
g{\phi\phi}=-r2 \sin(\theta)2
}.
complete(ss, $g^{\mu\nu}$);`
`ch:= \Gamma^{\mu}{\nu\rho} = 1/2 g^{\mu\sigma} (
\partial{\rho}{g{\nu\sigma}}
+\partial{\nu}{g{\rho\sigma}}
-\partial{\sigma}{g_{\nu\rho}} ):
evaluate(ch, ss, rhsonly=True);`
rm:= R^{\rho}_{\sigma\mu\nu} = \partial_{\mu}{\Gamma^{\rho}_{\nu\sigma}} -\partial_{\nu}{\Gamma^{\rho}_{\mu\sigma}} +\Gamma^{\rho}_{\mu\lambda} \Gamma^{\lambda}_{\nu\sigma} -\Gamma^{\rho}_{\nu\lambda} \Gamma^{\lambda}_{\mu\sigma}; substitute(rm, ch) evaluate(rm, ss, rhsonly=True);
ex:=K^{a}_{b}=R^{\mu}_{\rho\nu\beta}ei^{a}_{\mu}i^{\rho}_{t}i^{\nu}_{b}i^{\beta}_{t}; substitute(ex, rm) viel:={i^{t}_{t}=Q/f,i^{r}_{t}=-j,i^{\theta}_{t}=0,i^{\phi}_{t}=0,i^{t}_{r}=-j/f,i^{r}_{r}=Q,i^{\theta}_{r}=0,i^{\phi}_{r}=0,i^{t}_{\theta}=0,i^{r}_{\theta}=0,i^{\theta}_{\theta}=1/r,i^{\phi}_{\theta}=0,i^{t}_{\phi}=0,i^{r}_{\phi}=0,i^{\theta}_{\phi}=0,i^{\phi}_{\phi}=1/(r*\sin(\theta)),ei^{t}_{t}=f*Q*/((Q**2-j**2)),ei^{r}_{t}=-f*j/((j**2-Q**2)),ei^{\theta}_{t}=0,ei^{\phi}_{t}=0,ei^{t}_{r}=-j/((j**2-Q**2)),ei^{r}_{r}=Q/((-f**2+Q**2)),ei^{\theta}_{r}=0,ei^{\phi}_{r}=0,ei^{t}_{\theta}=0,ei^{r}_{\theta}=0,ei^{\theta}_{\theta}=r,ei^{\phi}_{\theta}=0,ei^{t}_{\phi}=0,ei^{r}_{\phi}=0,ei^{\theta}_{\phi}=0,ei^{\phi}_{\phi}=r*\sin(\theta)}; substitute(viel, $j=(Q**2-f)**(1/2)$) substitute(viel, $f=1-2*M/r + q**2/r**2$) evaluate(ex, viel, rhsonly=True);