General relativity in flat space-time

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.
• 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.