Classical mechanics
Given that
Coulomb's inverse-square law [1]
takes the form of
Newton's law of universal gravitation [2]
if we write:
It seems reasonable to explore the use of complex numbers, as a data structure,
to treat electrostatics in a gravitational context.
Given the assumption:
Mass would be:
A complex gravitational potential defined as:
would hold enouh information to describe the classical static interaction with a different body. Which could provide a framework to justify why
we don't seem to messure direct attraction/repulsion between
mass and charge, since the representation of this interaction
is caught in the imaginary part of:
Special Relativity
Consider a complex Momentum P
: mass energy contribution
: charge energy contribution
To write:
being:
Which points us to express magnetic phenomena in terms of P.
Electromagnetism
The description of Gravitoelectromagnetism [3]
already gives us a good picture of the pattern. Converting Coloumbs into Kilograms using the following convertion factor,
and allowing variables to be complex:
The full set of equations could be written as:
Subscripts m and e,
refer to massive and electric quantities.
References
6. Carlos Francisco Romero Madrid, Derivation of the Metric of Reissner-Nordström and Kerr-Newman Black Holes, 2018
7. Guansheng He, Exact Harmonic Metric for a Uniformly Moving Schwarzschild Black Hole
Article in Communications in Theoretical Physics · January 2014
261016243
8. Richard A. Hutchin, A Natural Combination of Gravity and Electromagnetism, Journal of Modern Physics, 2015, 6, 749-757
2015.66080
9. Bahram Mashhoon, Gravitoelectromagnetism: A Brief Review
0311030
10. Athanasios Bakopoulos, Gravitoelectromagnetism: Basic principles, novel approaches and their application to Electromagnetism
1610.08357