Thank you

@tomleslie

Works perfectly but i have some problem with a system of equations , i dont know what is wrong with thatpp.mw

@vv Thank you but the right diagram by analytical approach is very different. What's the point? 

@John Fredsted 

Thank you for your attention.

I have uptodated my answer..max.mw

@John Fredsted

I used your method for maxwell equation what do think about that?

I think i made mistake !

maxwell.mw

@ecterrab 

There is a generic problem in both of them(ss.mw and jj.mw)  i mean when you put H^2=H^3=..=0 (or g^2=..=0) you expect to have smaller result but with your method you will have very long resul. 

@ecterrab 

Dear Edgardo in JJ.mw i want to eliminate H(r)^2 ,H(r)^3,... but with frontend(series ,[ ]) i cant do it , please show me

@John Fredsted 

Thank you John. its perfect.

How to use your method for Maxwell equation ?

JJ.mw

@John Fredsted 

its a good way but  derivatives of g(r) and h(r) are presented in expr

@ecterrab @ecterrab 

Thank you for your reply.

i used frontend(series, [(17), g(r), 2]) but did not work.

JJ.mw

@ecterrab 

Yes i mean assigning values to the components of k , but i can not do it , even i can not do k_[]

@ecterrab 

Thank you for your points.

I have some questions , How can i put k components in 17 and how can i eliminate non-linear terms like g(r)^2 from 17 and how can we do this process for maxwell equation ?

small_perturbations_(reviewed).mw

for simplisity i consider phi(x)

@ecterrab 

thank you.

This is the solution i was chasing.

Dear @ecterrab 

I think components of the extrinsic curvature are not equal to zero

https://physics.stackexchange.com/questions/144164/gibbons-hawking-york-ghy-boundary-term-for-schwarzschild-metric

@John Fredsted yes I want to know what transform functions can provide this explicit forms. can maple find these transform functions? 

@ecterrab 

first of all thanks for your attention ,

what we are looking for is finding the transform function between coordinate systems. in our case , we have a metric with coordinates (M,J) and have another metric with coordinates ( t,x) but don't know M(x,t) and J(x,t) .

changecoor.mw