Einstein's constant

Einstein's constant or Einstein's gravitational constant, denoted κ (kappa), is the coupling constant appearing in the Einstein field equation which can be written:

<center><math>G^ = kappa , T^~</math></center>

where G^αγ is the Einstein tensor and T^αγ is the stress-energy tensor.

This equation relates to the curvature of space and time, telling that stress-energy is what causes the disturbance of spacetime, thus gravitation. Einstein used Newton's law of universal gravitation in his field equations, and the constant of κ is found to have a value of:

<center><math>kappa , = , - ~</math></center>

N.B.: Writing Einstein's constant depends on how the stress-energy tensor is defined, so the Einstein field equations are always invariant (see details in the section "About the two possible writings" further).

Calculation

In the following, the value of Einstein's constant will be calculated. To do so, at the beginning a field equation where the cosmological constant Λ is equal to zero is taken, with a steady state hypothesis. Then we use the Newtonian approximation with hypothesis of a weak field and low velocities with respect to the speed of light.

The Newton law will arise...
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