Energy as a complex number

Equations of gravity and electromagnetism exhibit structural similarities. After a convertion of units,
the pattern we see could be mathematically explained in terms of complex variables, this expression ends up capturing some aspects of both fields
in a compact notation.

: energy,

: mass,

: speed of light,

: complex unit,

: charge,

: vacuum permittivity,

: universal gravitational constant

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

1. Wikipedia, Coulomb's inverse-square law

2. Wikipedia, Newton's law of universal gravitation

3. Wikipedia, Gravitoelectromagnetism

4. Wikipedia, Minkowski metric

5. Wikipedia, Schwarzschild metric

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

This equation was first digitally written and cryptographically signed on Sep-04-2022 09:46:26 PM +UTC as shown in "decoded input data" in the "more details" section of the following link:

E = Y*(m + i*Q/(4*pi*e0*G)^(1/2))*C^2

This document is licensed under CC BY: Creative Commons Attribution

Marcelo Villarreal Fasanelli - emq.guy@gmail.com

E = Y*(m + i*Q/(4*pi*e0*G)^(1/2))*C^2

This document is licensed under CC BY: Creative Commons Attribution

Marcelo Villarreal Fasanelli - emq.guy@gmail.com