Einstein's constant

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

G^{\alpha \gamma }=\kappa T^{\alpha \gamma },

where $G αγ$ is the Einstein tensor and $T αγ$ is the stress–energy tensor.

This equation relates to the curvature of spacetime, indicating that stress–energy is what causes the curvature of spacetime, thus gravitation. The constant κ is directly related to Newton's gravitational constant $G$ :^[1]

\kappa ={\frac {8\pi G}{c^{2}}}\approx 1.866\times 10^{-26}\mathrm {\ m{\cdot }kg^{-1}} .

The above is for the stress–energy tensor in units of mass density (i.e., mass per volume). The units of 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

\kappa ={\frac {8\pi G}{c^{4}}}\approx 2.076\,579\times 10^{-43}\mathrm {\ s^{2}{\cdot }m^{-1}{\cdot }kg^{-1}\ (or\ m{\cdot }J^{-1}or\ N^{-1})} .

References

^ Adler, Ronald; Bazin, Maurice; Schiffer, Menahem (1975). "10.5: Classical Limit of the Gravitational Equations". Introduction to General Relativity (2nd ed.). New York: McGraw-Hill. p. 345. ISBN 0-07-000423-4.

References

Further reading