Question: How to define and evaluate a function of two tensors in Maple?

I am working with the de Sitter metric which takes the form 

$$g=\tau^{-2}\left(-\left(\Lambda / 3-\tau^{2}\right)^{-1} d \tau^{2}+\left(\Lambda / 3-\tau^{2}\right) d t^{2}+g_{\mathbb{S}^{2}}\right)$$

or 

g := evalDG((-`dτ` &t `dτ`/(Lambda/3 - tau^2) + (Lambda/3 - tau^2)*(dt &t dt) + (dtheta &t dtheta) + sin(theta)^2*(dphi &t dphi))/tau^2)

in the co-ordinates $\{\tau, t, \theta, \phi\}.$

or 

DGsetup([tau, t, theta, phi], M1, verbose)

Define

F := evalDG(-Q*(`dτ` &t dt) + Q*(dt &t `dτ`))

Then I want to define the following function which takes a two tensor (metric) and returns a two tensor as well. 

Here \dot(g) is the input tensor, F is the two tensor defined above and the g is the de Sitter metric. 

I want to evaluate this expression of \dot{g} = d tau^2/tau^2 and other metrics. How can I do this in Maple?

Any help will be much appreciated.