Extended gravitoelectromagnetism. I. Variational formulation

G. O. Ludwig

The European Physical Journal Plus volume 136, Article number: 373 (2021) Cite this article

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Abstract

This work presents a novel approach to well established concepts of gravity, formulating a new and consistent gravitoelectromagnetic theory. The long standing gravitoelectromagnetic field theory is considered in the framework of Hamilton’s principle. A variational formulation based on this principle describes the dynamics of a fully-relativistic perfect fluid in the presence of the gravitoelectromagnetic field in flat space, leading to the definition of the fluid and field energy-momentum tensors. A relativistic Cauchy invariant for a compressible fluid immersed in the gravitoelectromagnetic field is demonstrated. The gravitoelectromagnetic fluid equations of motion are written in covariant form suited for calculating higher-order relativistic effects. The integral form of the conservation theorems is presented, as well as equations that describe the excitation of gravitoelectromagnetic waves. As an application, the equations of motion are used to derive the equation that governs the galactic rotation according to gravitoelectromagnetism.

@neo Is this different than the article from Ludwig that I blogged previously at http://dispatchesfromturtleisland.blogspot.com/2021/04/dark-matter-phenomena-as-neglected.html ? It looks the same.

"The paper about gravitomagnetism is complete bunk. Not even wrong. I got enough questions about it that I started to write a post, but stopped after doing the most basic calculation. This effect scales as (v/c)^2 ~ (300 km/s/300,000 km/s)^2 [where the biggest spiral spins at 300 km/s] so this is at most a one part in a million effect. No way this solves the missing mass problem. I did read some of the paper, and spotted numerous problems. The M/L of NGC 1650 is still ridiculously high, for example, so hardly gets rid of the need for dark matter. Its rotation curve isn’t actually fit. There’s just no substance of value to this."

@neo This is definitely not the issue in Deur's approach which relies on graviton self-interaction in the weak field rather than gravitomagnetism. Also, its few citations, rather than zero, and the reason is pretty obviously that he's an outsider in the field.

One of the reason that I can be certain is that Deur is using a static approximation of gravity, essentially taking all of the pressure and momentum components of the stress-energy tensor to zero. Gravitomagnetism is a dynamic effect, for which non-zero momentum is the source.

This is why the phenomenological approximation in the form of MOND kicks in at such a weak acceleration (which is probably a second order gravitational self-interaction effect).

a0 = 1.2 x 10^-10 ms^-2

If the Sun were the only mass involved, this would kick in at 1/9th of a light year from the Sun (175 times as far away as Pluto). MOND double the Newtonian prediction for gravity at a distance of 2/9th of a light year from the Sun (again, ignoring external field effects).

## 9 comments:

btw

Extended gravitoelectromagnetism. I. Variational formulation

G. O. Ludwig

The European Physical Journal Plus volume 136, Article number: 373 (2021) Cite this article

8 Accesses

Metrics details

Abstract

This work presents a novel approach to well established concepts of gravity, formulating a new and consistent gravitoelectromagnetic theory. The long standing gravitoelectromagnetic field theory is considered in the framework of Hamilton’s principle. A variational formulation based on this principle describes the dynamics of a fully-relativistic perfect fluid in the presence of the gravitoelectromagnetic field in flat space, leading to the definition of the fluid and field energy-momentum tensors. A relativistic Cauchy invariant for a compressible fluid immersed in the gravitoelectromagnetic field is demonstrated. The gravitoelectromagnetic fluid equations of motion are written in covariant form suited for calculating higher-order relativistic effects. The integral form of the conservation theorems is presented, as well as equations that describe the excitation of gravitoelectromagnetic waves. As an application, the equations of motion are used to derive the equation that governs the galactic rotation according to gravitoelectromagnetism.

@neo Is this different than the article from Ludwig that I blogged previously at http://dispatchesfromturtleisland.blogspot.com/2021/04/dark-matter-phenomena-as-neglected.html ? It looks the same.

Ah. Looks like it is a different article in the same journal as the citation and title are different. I'll look.

from Triton Station in a comment to a post:

"The paper about gravitomagnetism is complete bunk. Not even wrong. I got enough questions about it that I started to write a post, but stopped after doing the most basic calculation. This effect scales as (v/c)^2 ~ (300 km/s/300,000 km/s)^2 [where the biggest spiral spins at 300 km/s] so this is at most a one part in a million effect. No way this solves the missing mass problem. I did read some of the paper, and spotted numerous problems. The M/L of NGC 1650 is still ridiculously high, for example, so hardly gets rid of the need for dark matter. Its rotation curve isn’t actually fit. There’s just no substance of value to this."

https://tritonstation.com/2021/04/12/divergence/#comments

i suspect Deur also has this problem - too weak like gravitomagnetism which is why it's has 0 citation

@neo This is definitely not the issue in Deur's approach which relies on graviton self-interaction in the weak field rather than gravitomagnetism. Also, its few citations, rather than zero, and the reason is pretty obviously that he's an outsider in the field.

One of the reason that I can be certain is that Deur is using a static approximation of gravity, essentially taking all of the pressure and momentum components of the stress-energy tensor to zero. Gravitomagnetism is a dynamic effect, for which non-zero momentum is the source.

the gravitational interaction of photons is extremely weak , gravitational waves are extremely weak so gravitons more so

my suspicion is Deur like gravitomagnetism is 1 million times too weak to explain dark matter

This is why the phenomenological approximation in the form of MOND kicks in at such a weak acceleration (which is probably a second order gravitational self-interaction effect).

a0 = 1.2 x 10^-10 ms^-2

If the Sun were the only mass involved, this would kick in at 1/9th of a light year from the Sun (175 times as far away as Pluto). MOND double the Newtonian prediction for gravity at a distance of 2/9th of a light year from the Sun (again, ignoring external field effects).

This is really meager.

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