Variation of an abstract matter Lagrangian

[Hendrik Ludwig]

Hi,

I am trying to derive equations of motion using VarL but I want to keep the matter Lagrangian "abstract", not composed of any explicit fields. I expect the variations w.r.t. the metric to be left "as is" so that I can later interpret them has Energy-Momentum-Tensor. But it does not work. I tried

Lm /: ImplicitTensorDepQ[Lm, met] = True

but VarL still throws away all variations of Lm w.r.t. met....

Is it not possible what I am trying to achieve?

Many, thanks in advance!

[Hendrik Ludwig]

P.S. a minimum working example:

xAct`xTensor`Commutator;
xAct`xTensor`Anticommutator;
Needs["xAct`xTras`"];
DefManifold[M4, 4, {a, b, c, d}];
DefMetric[-1, met[-a, -b], CD];
DefTensor[Lm[], M4];

Lm /: ImplicitTensorDepQ[Lm, met] = True

VarL[met[a, b], CD][Lm[]]

It gives only the volume term, not the variations of the matter Lagrangian "Lm" with respect to the metric "met".

[Hendrik Ludwig]

I solved it now with the usual xPert method and replacing the variation of the matter Lagrangian by hand, but it would be nice if VarL could also handle abstract matter Lagrangians