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This research aims to establish a constitutive law in weak-field gravity that accounts for the relaxation time of the geometric response.

July 23, 2026Open Access

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Spacetime Has a Relaxation Time: A Constitutive Completion of Weak-Field Gravity

ARAlejandro Rey

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This research aims to establish a constitutive law in weak-field gravity that accounts for the relaxation time of the geometric response.
Coarse-graining over galactic scales to derive a minimal constitutive law
Multi-regime tests across various astrophysical environments
Prediction of optical projection amplitude without fitting to lensing data
Optical projection amplitude A_rel predicted as 1.267, matching KiDS/GAMA weak-lensing measurement at 0.01σ
Consistent constitutive response observed across various tests, including rotation curves and cluster mergers
Provided a falsifiable effective theory that contrasts with traditional unseen mass interpretations

Abstract

Starting from the retarded solution of linearized General Relativity and coarse-graining over galactic scales, a minimal constitutive law emerges — one that requires no new particles, only a finite relaxation time for the weak-field geometric response. The same framework predicts, without fitting to lensing data, an optical projection amplitude Aᵣel = 19/15 = 1. 267, matching the KiDS/GAMA weak-lensing measurement at 0. 01σ. Multi-regime tests across galactic rotation curves, halo-mass benchmarks, strong lensing, radio-relic cluster mergers, and peculiar velocity environments all support the same constitutive response. The result is a compact, falsifiable effective theory in which dark-sector phenomenology is delayed weak-field geometry rather than unseen mass.

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Spacetime Has a Relaxation Time: A Constitutive Completion of Weak-Field Gravity

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