What does this research mean for the field?

Within the tested class of local metric and disformal constructions, a scalar field alone is insufficient to provide a viable relativistic completion of MOND that reproduces both galactic rotation curves and gravitational lensing; restoring the lensing channel requires additional preferred-structure degrees of freedom, such as a vector field. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To systematically evaluate whether relativistic completions of Modified Newtonian Dynamics (MOND) can successfully replicate the modified force law and gravitational lensing using minimal degrees of freedom without requiring complex vector fields.

August 30, 2026Open Access

An Obstruction Map for Relativistic MOND: the Conformal Lensing Barrier and the Cost of Its Repair

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Authors

CZCarl P. ZimmermanAd-Tech (United States)

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Implication

Theoretical analysis demonstrates that screened scalar completions of modified gravity fail gravitational lensing tests, indicating that relativistic models require additional vector degrees of...

Key Points

To systematically evaluate whether relativistic completions of Modified Newtonian Dynamics (MOND) can successfully replicate the modified force law and gravitational lensing using minimal degrees of freedom without requiring complex vector fields.
Conducted a systematic closure analysis across seven local metric and Hamiltonian architectures against Hojman–Kuchař–Teitelboim uniqueness conditions.
Evaluated screened (k-mouflage/Vainshtein) scalar-tensor models against parameterized post-Newtonian limits, tensor speed bounds from GW170817, and solar system constraints.
Performed a committed 175-galaxy parameter scan assessing the Cassini external-field quadrupole against wide-binary velocity enhancements (γv).
Conformally coupled scalar fields fail to bend light due to the conformal invariance of null geodesics, predicting galaxies that rotate dynamically under MOND but lens light only according to bare baryonic mass.
Cassini-safe screening kernels that satisfy solar system quadrupole ceilings (μ5/μ10 clearing at 0.39 and 0.08) concurrently suppress the wide-binary velocity ratio to γv ≈ 1.0001–1.0040, far below the expected 1.16–1.23 signal.
Restoring proper gravitational lensing requires a disformal coupling with preferred timelike structures, demonstrating that relativistic MOND necessitates extra vector degrees of freedom rather than simpler scalar completions.

Cite This Study

Carl P. Zimmerman (2026) studied this question.

synapsesocial.com/papers/6a93f0f56c1a8fb52e79d85e https://doi.org/10.5281/zenodo.22135510

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Implication

Theoretical analysis demonstrates that screened scalar completions of modified gravity fail gravitational lensing tests, indicating that relativistic models require additional vector degrees of...

An Obstruction Map for Relativistic MOND: the Conformal Lensing Barrier and the Cost of Its Repair

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Implication

Key Points

Cite This Study

An Obstruction Map for Relativistic MOND: the Conformal Lensing Barrier and the Cost of Its Repair

Discussion

Member takes

Implication

Key Points

Cite This Study

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