Question: Covariant Derivative and Covariant Tensor and Contravariant Tensor

guys , i have a metric and i want to define a componenets of a tensor and then obtain its covariant derivative with respect to a metric, what is your idea ?

N_1=-A(r)^1/2 , A_2=A_3=A_4=0 , what is D_[nu] N_1 =?

 in general i want to define N[1]=-A(r)^(1/2) and N[2] = N[3]= N[3] = N[4] = 0 And define F[mu, nu] = 2*(D_[mu] N[nu]-D_[nu] N[mu]) And define Omega[mu, nu] = 2*(D_[mu] N[nu]+D_[nu] N[mu]) and compute expression F_[alpha, beta] F_[~alpha`, ~beta ] And N_[alpha] N_[~beta`] F_[ ~alpha, ~lambda ] Omega_[beta, lambda])

i have problem with this how to difine this tensorial terms and how to compute them.



Please Wait...