Dark Energy

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These are questions asked by Dark Energy

Hello guys,

Assume we have metric ds^2=a(r,t)*dt^2-b(r,t)*dr^2-r^2*dtheta^2-r^2*sin^2(theta)*dphi^2 wherein a(r,t) and b(r,t) are two arbitrary metric functions. how we can find 4-vector velocity for comoving and independent observers?

with best

hi guys,

suppose we have general metric form in 4-D. I want to calculate Covariant derivative of Riemann, Ricci and Weyl tensors.

please help me.

with best,

Hi guys,

I know how to plot inequality system through using with(plots) and inequal term. however, I couldn't plot following system of inqulity equations:

alpha <= 0.0002500000000*(-18000.*m^2 + 47271.*m + 39514. + sqrt(3.24000000*10^8*m^4 - 1.701756000*10^9*m^3 - 4.266980559*10^9*m^2 - 3.036299412*10^9*m - 6.95987804*10^8))/(9.*m^2 + 12.*m + 4.), 0.00005000000000*(-90000.*m^2 + 237237.*m + 198158. + sqrt(8.100000000*10^9*m^4 - 4.270266000*10^10*m^3 - 1.069976858*10^11*m^2 - 7.612670111*10^10*m - 1.744924704*10^10))/(9.*m^2 + 12.*m + 4.) <= alpha, -0.6666666667 < m, m < -0.6665522013

please let me know how we can plot it.

with best

Hi guys,

suppose we have metric in curve geometry such as ds2=A(r)*dt^2-B(r)*dr^2+r^2*dtheta^2+r^2*sin^2(theta)*dphi^2.

how we can calculate and find exact not symbolic different components of contravariant derivative of contravariant derivative of Weyl tensor and Riemann tensor.

with best regards,

Hello guys,

I want to find exact form of a(t) in following differential equation:

-diff(a(t), t)^2*_C1*6^(-1/(-1 + 2*alpha))*((diff(a(t), t, t)*a(t) + diff(a(t), t)^2)/a(t)^2)^(-1/(-1 + 2*alpha))/(4*(diff(a(t), t, t)*a(t) + diff(a(t), t)^2)*(-1/2 + alpha)) = (6*diff(a(t), t, t)*a(t)^2*alpha + 6*a(t)*diff(a(t), t)^2*alpha + k^2)/a(t)^3

please guide me,

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