Einstein's Constant

# Einstein's constant

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Description:
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>[itex]G^ = kappa , T^~[/itex]</center>

where G<sup>αγ</sup> is the Einstein tensor and T<sup>αγ</sup> 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>[itex]kappa , = , - ~[/itex]</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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