Help needed on a problem related to Kaluza Klein Theory

[Rahul Kothari]

Dear all,

I'm working on a problem related to Kaluza Klein theory. I need to define different components of a 5D tensor in terms of some 4D tensors. For example, I would like to define the 5D metric in the following manner (Snapshot from Particle Physics and Cosmology by Collins et.al.)

I found a related solution on the Mathematica Stackexchange website

https://mathematica.stackexchange.com/questions/166311/define-tensor-made-of-other-tensors-in-xact/166403#166403

I tried this but this isn't helpful as this gives out the 5D tensor and not the 4D tensor in terms of which it is to be described. 

Another problem arises when I try to put g_{55} = \phi^{-1/3}*\phi. Please help me implementing this in xAct.

Any help would be highly appreciated.

Thanks in advance

--

Rahul Kothari (राहुल कोठारी)

Post Doctoral Researcher

Department of Physics and Astronomy

The University of the Western Cape,

South Africa

Transire suum pectus mundoque potiri.