A gravity tensor and gauge equations for Newtonian dynamics
A gravity tensor and gauge equations for Newtonian dynamics
It is revealed that the material derivative of a variable in gravity field is its directional derivative, from which and energy/complementary-energy conservations with exterior derivatives, two sets of gauge equations of Newton’s dynamic gravity field are derived, which has same mathematical structure with the gauge ones for the Maxwell equations in electromagnetic fields, revealing that gravity force and curl momentum in Newton’s gravity field, respectively, play the roles like the electric E and the magnetic B of the Maxwell equations in the electromagnetic field . The gravity tensor of Newton’s gravitational field is constructed, and an example is given to validate it. This finding allows Newton’s gravity to be governed by a gauge theory, addressing the historic issue that “Newton’s gravitation is an exception to the Yang–Mills gauge theory”.
gravity tensor; gauge equations of the gravity field; Newton’s gravity field; exterior derivatives; energy conservation; energy-flow equation
Xing, Jing T
d4fe7ae0-2668-422a-8d89-9e66527835ce
9 January 2026
Xing, Jing T
d4fe7ae0-2668-422a-8d89-9e66527835ce
Xing, Jing T
(2026)
A gravity tensor and gauge equations for Newtonian dynamics.
Axioms, 15 (1), [51].
(doi:10.3390/axioms15010051).
Abstract
It is revealed that the material derivative of a variable in gravity field is its directional derivative, from which and energy/complementary-energy conservations with exterior derivatives, two sets of gauge equations of Newton’s dynamic gravity field are derived, which has same mathematical structure with the gauge ones for the Maxwell equations in electromagnetic fields, revealing that gravity force and curl momentum in Newton’s gravity field, respectively, play the roles like the electric E and the magnetic B of the Maxwell equations in the electromagnetic field . The gravity tensor of Newton’s gravitational field is constructed, and an example is given to validate it. This finding allows Newton’s gravity to be governed by a gauge theory, addressing the historic issue that “Newton’s gravitation is an exception to the Yang–Mills gauge theory”.
Text
axioms-15-00051
- Version of Record
More information
Accepted/In Press date: 30 December 2025
Published date: 9 January 2026
Keywords:
gravity tensor; gauge equations of the gravity field; Newton’s gravity field; exterior derivatives; energy conservation; energy-flow equation
Identifiers
Local EPrints ID: 509435
URI: http://eprints.soton.ac.uk/id/eprint/509435
ISSN: 2075-1680
PURE UUID: 57bb93d9-c502-4646-8ad5-882cb35619d8
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Date deposited: 23 Feb 2026 17:37
Last modified: 07 Mar 2026 02:42
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