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Updated: Apr 8, 2026

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General relativity in flat space-time.

Serge Aubry1

  • 1Institute of Theoretical and Computational Physics and Department of Physics, University of Crete, Heraklion 71003, Greece.

Chaos (Woodbury, N.Y.)
|April 7, 2026
PubMed
Summary
This summary is machine-generated.

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This study revisits Einstein

Area of Science:

  • Theoretical Physics
  • Gravitation
  • Cosmology

Background:

  • Einstein's General Relativity (GR) describes gravity using a Lagrangian in Minkowski spacetime.
  • GR presents black hole horizons as singularities where light speed is not constant.
  • The principle of mass-energy equivalence suggests physical quantities rescale with gravitational potential.

Purpose of the Study:

  • To re-examine fundamental concepts of General Relativity.
  • To derive a novel Lagrangian for static gravitational potentials.
  • To develop a transformation method for generating fully relativistic Lagrangians.

Main Methods:

  • Rescaling physical quantities (rest mass-energy, time, light speed) based on gravitational potential.
  • Deriving a 'germinal' Lagrangian for static gravitational potentials.

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  • Transforming the germinal Lagrangian into a fully relativistic form using a novel method.
  • Main Results:

    • A new static gravitational Lagrangian (germinal) is obtained, distinct from Schwarzschild but sharing its black hole singularity.
    • The transformation method yields a fully relativistic gravitational Lagrangian with a 4x4 tensor potential.
    • In the weak field limit, the generated Lagrangian resembles Heaviside's theory but is fundamentally different.

    Conclusions:

    • The proposed theory, while not equivalent to GR, offers a new framework for gravitation.
    • The derived Lagrangian explains galactic stellar velocity anomalies without invoking dark matter.
    • This approach provides a potential alternative to dark matter in cosmological models.