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: 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: where Gαγ is the Einstein tensor and Tαγ 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 directly proportional to Newton's gravitational constant G: The above is for the stress-energy tensor in units of mass density (i.e., mass per volume). Writing Einstein's constant depends on how the stress–energy tensor is defined, so an alternative choice for T with units of energy density (i.e., energy per volume) yields (see § About the two possible forms below for details). 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 and its corollary Poisson's equation. In this approximation, Poisson's equation appears as the approached form of the field equation (or the field equation appears as a generalization of Poisson's equation). The identification gives the expression of Einstein's constant related to quantities G and c. We have to obtain a suitable tensor to describe the geometry of space in the presence of an energy field. Einstein proposed this equation in 1917, written as: