Strange behaviour of SeparateMetric

[Markus B. Fröb]

Hi all,

I ran into an infinite recursion in xPert (latest version) under Mathematica 11.1, when using ExpandPerturbation on a perturbed metric with contravariant indices: ExpandPerturbation[Perturbation[g[a,b],1]] (without having used DefMetricPerturbation before).

The issue seems to be that SeparateMetric[][g[a,b]] returns g[b,a], which seems quite strange.

I think that SeparateMetric when called without an explicit index to separate should leave any explicit metric tensors untouched. Would you agree?

The fix in this case is simple: replace in section "14.2.5. SeparateMetric. New code" the function

SeparateMetric[metric_, basis_][expr_, Automatic] := 

  With[{tensors = FindAllOfType[expr, Tensor], covds = FindAllOfType[expr, CovD]}, 

   SeparateMetric[metric, basis][expr, Flatten@Apply[IndexList, movedindices /@ Join[tensors, covds]]]

  ];

by

SeparateMetric[metric_, basis_][expr_, Automatic] := 

  With[{tensors = FindAllOfType[expr, Tensor], covds = FindAllOfType[expr, CovD]},

   Module[{tensors2},

    If[metric === Automatic, tensors2 = DeleteCases[tensors, _?(MetricQ[Head[#]] &)], tensors2 = DeleteCases[tensors, _metric]];

    SeparateMetric[metric, basis][expr, Flatten@Apply[IndexList, movedindices /@ Join[tensors2, covds]]]

   ]

  ];

Best, Markus

[Jose]

Thanks for reporting this Markus.

You are very right that SeparateMetric should not try to separate metric factors from the first-metric itself (independently of whether that metric was specified in the first pair of brackets or not). Instead of the code you included in your email, I prefer to add this explicit case before the general definition of SeparateMetric2:

SeparateMetric2[AIndex, metric_][metric_[i1_, i2_], index_] := metric[i1, i2];

Cheers,

Jose.

[Markus B. Fröb]

Hi Jose,

that one works as well. Thanks!

(Sorry for not answering earlier - I didn't get any notification from your reply, and in the meantime was busy.)

I have another strange behaviour to report, with the xPert package.

Defining a metric g and perturbation h, ToCanonical[ h[LI[1], -a, -b] Perturbation[ g[c,b] ] ] returns 0.

It seems that this is due to ToCanonical reordering the indices to h[LI[1], -a, b] Perturbation[ g[c,-b] ], and then Perturbation[ g[c,-b] ] = Perturbation[ delta[c,-b] ] = 0.

I haven't come up with a fix for this one, though, and for the moment just make sure to ExpandPerturbation[] everywhere.

Best, Markus