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The aim is to derive foundational aspects of general relativity from a single geometric principle named worldline non-injectivity.

April 17, 2026Open Access

Tidal Forces, the Equivalence Principle, and the Emergence of the Einstein Field Equations from Worldline Non-Injectivity in de~Sitter Spacetime

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Derives tidal forces and the equivalence principle in de Sitter spacetime, indicating their geometric origin.

The aim is to derive foundational aspects of general relativity from a single geometric principle named worldline non-injectivity.
Derivation of tidal forces from proper-time gradients across extended bodies.
Topological averaging of a Lorentz-scalar Lagrangian derived from proper-time field.
Logical derivation of the equivalence principle in classical and quantum contexts.
Analysis conducted in de Sitter spacetime.
Tidal forces linked to proper-time gradients produce a strain tensor matching the electric part of the Weyl tensor.
Einstein field equations derived from the average of a Lorentz-scalar Lagrangian.
Cosmological constant expressed as finite and independent of UV cutoff.
Quantum corrections predict a detectable violation of the Weak Equivalence Principle.

Alex De Giuseppe (2026) studied this question.

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