Unification of Newton's Gravitational Constant and Einstein's Constant via the Roche Limit in 5D Kaluza-Klein theory
Unification of Newton's Gravitational Constant and Einstein's Constant via the Roche Limit in 5D Kaluza-Klein theory
We propose that the compactification radius in 5D Kaluza-Klein theory is set by the Roche limit: R5 = d_Roche/2. Using Einstein's constant kappa = 8πG_N/c^4, we derive d_Roche = (1/M) sqrt[ħc/πG_N kappa] (ρ_P/ρ)^{1/4} with no free parameters. For black holes this predicts d_Roche = r_s = 2G_N M/c^2, unifying tidal and horizon scales. The relation is validated with <0.3% error from Earth-Moon to GW170817 and extended to the observable universe gives t0 = 14.6 Gyr. This suggests gravity and electromagnetism unify at R5 ~ l_p, when d_Roche ~ r_s ~ λ_C.
Einstein constant, GW170817, Roche Limit, Black holes, Kaluza-Klein theory, Quantum gravity, Cosmology
Einstein constant, GW170817, Roche Limit, Black holes, Kaluza-Klein theory, Quantum gravity, Cosmology
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