- #1
sergiokapone
- 306
- 17
Suppose we have Einstein equation for *Universe free of matter* in form
\begin{equation}
G_{ik} = \chi T_{ik},
\end{equation}
where the cosmological constant $\Lambda$ is transferred to the RHS of equation and written in the form of stress–energy tensor of Dark Energy:
\begin{equation}\label{1}
T_{ik} = \begin{bmatrix}
\rho & 0 & 0 & 0 \\
0 & \rho & 0 & 0 \\
0 & 0 & \rho & 0 \\
0 & 0 & 0 & \rho
\end{bmatrix}
\end{equation}
Also, we can introduce the stress–energy pseudotensor of gravitation field in form of Landau-Lifshitz $t^{ik}$ and figure out:
\begin{equation}\label{2}
\frac{\partial }{\partial x^k} (-g) (T^{ik} + t^{ik}) = 0.
\end{equation}
Is it possible to find an expression for ##t^{ik}## pseudotensor, not counting it by the general formula from Landau-Lifshitz?
\begin{equation}
G_{ik} = \chi T_{ik},
\end{equation}
where the cosmological constant $\Lambda$ is transferred to the RHS of equation and written in the form of stress–energy tensor of Dark Energy:
\begin{equation}\label{1}
T_{ik} = \begin{bmatrix}
\rho & 0 & 0 & 0 \\
0 & \rho & 0 & 0 \\
0 & 0 & \rho & 0 \\
0 & 0 & 0 & \rho
\end{bmatrix}
\end{equation}
Also, we can introduce the stress–energy pseudotensor of gravitation field in form of Landau-Lifshitz $t^{ik}$ and figure out:
\begin{equation}\label{2}
\frac{\partial }{\partial x^k} (-g) (T^{ik} + t^{ik}) = 0.
\end{equation}
Is it possible to find an expression for ##t^{ik}## pseudotensor, not counting it by the general formula from Landau-Lifshitz?