How did Einstein know where to put individual elements of E-M Tensor $T$ w.r.t. the corresponding tensor $G$? where $G=kappa T$

Question

We know the well known relation in General Relativity.
$G=kappa T$
Where G is the Einstein Tensor and T is the Energy-Momentum Tensor and K is the constant.
I wanted to ask how did Einstein got to know where to place a particular element of a energy-momentum tensor with respect to the corresponding curvature tensor?
I know that for T(0,0) is the energy density which corresponds to the G(0,0) curvature tensor which gives the newtonian picture in rest frame. But how did Einstein got to know where to put what element of the T with respect to the curvature tensor G?
Any insight would be super helpful. Thanks!

G. Smith · Accepted Answer

The divergence of the energy-momentum-stress tensor is zero. The time component of this expresses energy conservation, and the spatial components express momentum conservation. This means that the time-time component is energy density, the time-space components are energy flow / momentum density, and the space-space components are momentum flow.
The components cannot be arbitrarily arranged inside the tensor. They are arranged in a way that they transform properly under local Lorentz transformations. For example, if the tensor has nonzero energy density but zero momentum density in a rest frame, it has to have nonzero momentum density in a moving frame.

How did Einstein know where to put individual elements of E-M Tensor $T$ w.r.t. the corresponding tensor $G$? where $G=kappa T$

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