@tomleslie

I am soory for the late. at the maple file attached here I describe the procedure  step by step. I hope it has enough clarification.

Thank you for your time

numericalode.mw 

@tomleslie 

First of all, I really appreciate your help.

I know what is happening physically but dont know how to translate to maple language.

let me try to explain what is happening there ,

we have a differential equation (3.3) ( i replaced theta by t ) , you solved numerically ( with your values for paramters M,l,C,Q,a,w) and find r against t diagram . now auther insert that in (3.2) then integrated  ( with theta_0=0.16 and r(0.159) ) and studied the relation between (3.2) and (2.6 T not t) that is figure 3 .

well how to find r(t) from your plot and integrate (3.2)

thank you for your help

@tomleslie 

actually this differential equation is equation 3.3 In the below paper which authors solved numerically..

https://arxiv.org/abs/1512.08855

@ecterrab 

thanks for the point you indicated , it was really crucial point .

considering your point i did two example , i think i have problem with one of them.

example.mw

thanks in advance

@ecterrab 

uptodated worksheet

tensor_correct.mw

still no answer !!

@Carl Love  @tomleslie @Preben Alsholm

my goal is to find the values of alpha and beta and gamma and lambda so that can solve equations ( de2.mw and correced.mw). so now i have two equations f(alpha,beta,gamma,lambda,w)=0 and g(alpha,beta,gamma,lambda,w)=0 by de2.mw and corrected.mw respectively , so there is exist the values of alpha and beta and gamma and lambda so that can solve de2 and corrected equations ?

how can i check this case ?

thank you guys

@tomleslie @Preben Alsholm

i have 5 differential equation which this one is one of them , so this differential equations are very complicated i guess a solution as above and put in equations to see what's happening.

this one is another one and i did your method for getting better looking result but still it has ugly face !

** i corrected the worksheet corrected.mw**

diff(A(r),r)^2 is correct or (diff(A(r),r))^2 for A'^2 ?

can numerical method for differential equation help us for this equations ?

thank you in advance guys

@tomleslie 

thanks so much , its looking so pretty now . i see Q ( its a constant , actually it is phi_0) is not involved in result equation , is not it strange ?

i reinstalled maple and the problem solved !

@ecterrab 

well i obtained the variation of the action i attached with respect to g_[~mu,~nu] but want to know that it is correct or not.

N[mu](x[~nu]) is unit time like four velocity and phi is brans-dicke scalar field and acction is written with Lorentzian signature(-,+,+,+)and omega is dicke constantaction.mw

thank you for your time.

best regards

@Torre in general i mean can we obtain the field equation of an action by variation ? e.g. f(R) gravity.

@ecterrab for (3) i obtained different solution mmm.mw . what is my problem ?

thxx

@ecterrab thank you for your comprehensive help. i appricione of the my problem now is how to define f(R) which R is function of a(t) that contravariant derivative or covariant derivative consider its dependence to t . eg. its easy to compute 00 and 11 components of the field equations that i attached handy. T_00 = rho_m+rho_r and T_11=0. and F is derivative of f with respect to R. but how can i define them so that 00 and 11 components of field equations obtain as the pic i attached.

guys with which command and how to calculate for example μ=0 and ν=0 for R_μρνσ+R_ρν g_σμ-R_ρσ g_νμ-R_μν g_σρ+R_μσ g_νρ +R[g_μν g_σρ -g_μσ g_νρ] Covariantderivative^ρ Covariantderivative^σ  f.  where f is a function of R. for a (-dt+dx+dy+dz) metric

thx again and again