What question did this study set out to answer?

This research aims to unify Newton's gravitational constant and Einstein's constant through the Roche limit in a higher-dimensional framework.

June 4, 2026Open Access

Unification 5 Campos Newton's Gravitational Constant and Einstein's Constant via the Roche Limit in 5D Kaluza-Klein theory

Key Points

This research aims to unify Newton's gravitational constant and Einstein's constant through the Roche limit in a higher-dimensional framework.
Proposed a relation between Roche limit and compactification radius in 5D Kaluza-Klein theory.
Derived formulas relating density, gravitational constants, and black hole properties with no free parameters.
Validated equations with <0.3% error across various astrophysical scenarios.
Predicted Roche limit d_Roche equals the Schwarzschild radius r_s for black holes, enabling unification at that scale.
Validated relationships from Earth-Moon distances to gravitational waves (GW170817), achieving high accuracy.
Extended findings to the observable universe, predicting a timeline of t0 = 14.6 Gyr for cosmic evolution.

Abstract

We propose that the compactification radius in 5D Kaluza-Klein theory is set by the Roche limit: R5 = dRoche/2. Using Einstein's constant kappa = 8πGN/c⁴, we derive dRoche = (1/M) sqrtħc/πGN kappa (ρP/ρ) ^1/4 with no free parameters. For black holes this predicts dRoche = rₛ = 2GN M/c², 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 ~ lₚ, when dRoche ~ rₛ ~ λC.

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Demicheri et al. (Tue,) studied this question.

synapsesocial.com/papers/6a2117fdd499ed480b170cdc https://doi.org/https://doi.org/10.5281/zenodo.20510142

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