The Einstein gravitational constant (Κ) is usually written as;    Κ = 8πG/c⁴ 

Can this constant be represented as wave-particle ratios of forces?

Is there any reference in the literature to these ratios? 

The ratios may be defined as follows.

Assume;              Κ = R_Thermal/R_Particle

Where;                 R_Thermal is a ratio of thermal forces (wave forces)    R_Thermal = F_TP/F_TH

                                

                            R_Particle is a ratio of particle forces       R_Particle = F_P/F_P0

A force magnitude (F_n) may be defined as; F_n = E_n²/ħc

Where;            E_n is energy

ħ is the reduced Plank constant (fundamental angular momentum)

c is the light constant

The thermal force definitions are;       F_TP = (k_BT_P)²/ħc 

F_TH = (hc/λ_H)(k_BT_H)/ħc 

Where;             k_B is the Boltzmann constant

T_P is Plank temperature

T_H is Hawking temperature

h is the Plank constant

ħ is the reduced Plank constant (ħ = h/2π)

λ_H is wavelength

The particle force definitions are;       F_P is Plank force  

F_P0 = E_P0²/ħc       

Where;             E_P0 = m_PG^½ 

m_P is Plank mass 

G is the gravitational constant

The ratio of force ratios gives the invariant ‘Κ’ ;        Κ(F_P/F_P0) = (F_TP/F_TH)

ΚR_Particle = R_Thermal 

Thermal energy requires;   hc/λ_H = mc² 

What is the significance of E_P0?

Thanks