@tomleslie 

Thank you for your responese. your guesses are right and excuse me because of bothering you by many errors in the worksheet. There is just two points I have to mention: 1- in differential equation you misse a 2 in power at the last term. when I added to the note it doesn't work. I don't know why. 

2- If I want f=1 why it doesn't work?

PS: I write both above cases in the worksheet attached here

Thanks again       numode2.mw 

@Torre 

with this approach , how we can compute dAlembertian(psi(t)) or D_[~mu](D_[nu](psi(t))) or a tensorial term like g_[mu,nu]  D_[~alpha](psi(t)) D_[alpha](psi(t)) with above metric, where psi(t) is a scalar function of time.

thanks in advance 

@ecterrab 

waiting for you

thanks so much

@ecterrab 

dear ecterrab , i want to compute D_[~2]F[2,1] but i have problem with it :D_[~2]F[2_1].mw

also i have computed D_[mu]D_[~mu] (N[1]N[1]phi(r)) with yout instructions , is it true ?.N[1]N[1]phi(r).mw

thank you for your time

Best regards

Covariant_wrong.mw

@ecterrab 

thank you for your help. i obtained different result handy for Omega[] !!! my result and maple result differ by a nagative sign!!!

i'm totally confused!!! 

dalembertian.mw i didnt compute yet, is there anybody who can help me ?

@escorpsy  

good question. @ecterrab , in this action , how to define scalar field and ... to able for variat with respect to g[~mu,~nu] ?

@ecterrab  thank you.

do you mean 1=t , 2=r , 3=theta and 4=phi ?

is it correct for christoffel t(up) r,r(down) to write Christoffel[~1,2,2] ?

@Torre thank you for your help.In general can we say  Ricci scalar has the same representation in both frame, because it is  scalar ?

@ecterrab thank you so much for your time , let me explicitly explain what i mean. in the above paper, term (4) is our original metric , with new basis (9) and (10) , we have the new metric (11). i want to for example calculate R_22 for (11).  R_22 for (4) is 2w^2-m^2 as you already calculated.

thanks again

@ecterrab thanks , i'm using maple 17 so i'll uptodate my maple to the latest version of Physics. the question that bothers me now is we can transform this metric to the locally lorentzian basis but how to find for example R_22 in this new metric ? thank you for your help.transformed_metric.mw

@ecterrab thank you for your help , my solution of (3) is something else as escorpsy said .

@ecterrab i have a metric , and want to compute some tensor term :

mm.mw

@ecterrab thank you for your help

@ecterrab for R_0,rho,alpha,beta R_0^rho,alhpa,beta , the term i wrote is correct ? and for R_1,rho,alpha,1 R^rho,alpha , Riemann[1,rho,alpha,1].Ricci[rho,alpha] is correct ?

thannks