Perturbation around Minkowski spacetime

[Vahid Nikoofard]

Hi everyone!

I am completely new to xAct world, so I hope my simple question doesn't bother you!

I am trying to calculate the weak field limit of EH gravity coupled to a scalar field around Minkowski metric using xPert. As everybody knows 

g_{\alpha \beta}= \eta_{\alpha \beta}+\epsilon h_{\alpha \beta}  

During the calculation I encounter some terms in the schematic form

\nabla_{\alpha} \partial_{\beta} \phi

where \phi is a scalar field, \nabla and \partial are covariant and partial derivatives, respectively. To implement the above term I define a scalar field by 

DefTensor[scalar[], M, PrintAs -> "\[Phi]"]

and put its perturbation to zero by

 

DefTensorPerturbation[0, scalar[], M]

Sincerely, I don't know whether these command are suitable or not! But As it can be seen from the attach notebook, in the out[10], the Mathematica doesn't understand it. 

My first question is how to tell this to Mathematica.

My second question is about the perturbation of square root of determinant of the metric, \sqrt{-g}, in the ln[11]. How can I say to Mathematica that \tilde{\tilde{-g}} is equal 1. 

Regards