Einstein gravitational constant

The Einstein gravitational constant \kappa appears in the Einstein Field Equations

G_{\mu \nu} + \Lambda g_{\mu \nu} = \kappa T_{\mu \nu}.

The constant gives the maximum force potential while the stress-energy tensor T_{\mu \nu} acts as a proportionality operator reducing the maximum potential in the right proportions to produce the gravitational force.

The Einstein gravitational constant is defined by the following relationship between the composite gravitational constant and the speed of light

\kappa = \displaystyle\frac{8 \pi G}{c^4}.

Restating the gravitational constant in fundamental units gives the following simple form of the Einstein gravitational constant

where F_P is the Planck force. The constant is derived by replacing G with fundamental Planck units

\kappa = 8 \pi \displaystyle\frac{G}{c^4} = 8 \pi \left( \displaystyle\frac{l_P^3}{m_P t_P^2} \right) \left( \displaystyle\frac{t_P^4}{l_P^4} \right) = 8 \pi \left( \displaystyle\frac{\cancel{l_P^3}}{m_P \cancel{t_P^2}} \right) \left( \displaystyle\frac{\cancel{t_P^2} t_P^2}{\cancel{l_P^3}l_P} \right) = 8 \pi \displaystyle\frac{t_P^2}{l_P m_P} = \displaystyle\frac{8 \pi}{F_P}.

The elementary form of the Einstein gravitational constant is

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