The task of the gravitational field of a material point taking into account the mass of the gravitational field itself

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Consider the problem of the gravitational field of a point mass, taking into account the mass of the gravitational field itself. First, assume that the mass of the gravitational field is negative and its density is -g^2/c^2. From the Gauss theorem, we write a differential equation for the gravitational field strength. The solution of this equation Otherwise it can be written where radius  of Shvartsald

if r<R=2Gm/c^2 one can use the asymptotic approximation of Bessel functions then we come to the classical formula of Newton's law of universal gravitation If we assume that the density of the gravitational field is positive and equal to g^2/c^2 then the solution of the corresponding differential equation is as follows Hence it can be seen that the corresponding differential equation for the positive mass of the gravitational field has no solution

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Moderator Note

Moved to Speculations.

Your posts would be readable if you used Latex rather than posting giant images.

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Do you pay special attention to units (dimensions) used in your equations? i.e. units on the left side of equation must match the right side of equation.. It's called dimensional analysis.

Take for example your the first equation. What is unit of dg and g? Is not the same units/dimensions? (r is in meters, and c is in m/s, obviously) If yes, then how come you have dg/dr on the left and g/c2 on the far right?

Edited by Sensei
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Do you pay special attention to units used in your equations? i.e. units on the left side of equation must match the right side of equation..

Yes the dimensions match

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Just now, SergUpstart said:

Yes the dimensions match

How? What are units/dimension of dg and g?

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I see an error in the first equation, the last term must be g^2/c^2. But the solution is given just for the second term of g^2/c^2

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28 minutes ago, Strange said:

Your posts would be readable if you used Latex rather than posting giant images.

He put them on his own website.. so he will be able to remove/modify/change them at any time... but I made screen-shots, just in case, if they will "magically" change content..

Edited by Sensei
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Why do you have $\frac{2GM}{r^3}$ when the central potential gravitational force is well tested using $F=\frac{2GM}{r^2}$ ?

As you can see latex is far more elegant.

Or is the r^3 a typo ?

Edited by Mordred
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Moderator Note

It would be much appreciated if you could switch to using Latex. Those giant images make your posts difficult to read. We have a thread available if you require help in using it, and you are welcome to make use of the Sand Box to test things out.

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1 hour ago, SergUpstart said:

In the topmost equation? Exactly 2Gm/r^3. It is a derivative by r of Gm/r^2. Dimension of g is m/s^2 and dg/dr is 1/s^2

Gauss's theorem popped up under the answer. I first uploaded the image, but failed to reduce or delete. Excuse me.

Still not following even under Gauss law gravity follows the inverse square law. Secondly how do you have a negative mass.

Mass is resistance to inertia change. So the very formula f=ma would behave quite differently with a negative mass.

Think of it this way let's assume one mass could possibly be negative while the other positive.

$m\dot a=\frac{GMm}{r^2}$ therefore $a=\frac{GM}{r^2}$ the mass term of the test object in essence does not matter.

Edited by Mordred
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I made a differential equation for both positive and negative gravitation field mass. It turned out that for a positive mass it has no solution, and for a negative one there is a solution and if the distance from the center of gravity is greater than The Schwarzild radius this solution converges asymptotically to the inverse square law g=Gm/r^2

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We cross posted see the equations I posted above. Then seriously think about the definition of mass then equate that to what a negative mass would entail.

Ie if you push a negative mass it would move in the opposite vector direction.

Edited by Mordred
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Just if the mass of the gravitational field is positive it means that the gravitational field strengthens itself, and the negative mass of the gravitational field means that it does not strengthen itself, but weakens

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You would first have to prove negative mass is possible without violating the conservation laws of energy momentum. Good luck with that.

Under GR negative mass is impossible.

Edited by Mordred
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What do you think about zero-energy Universe model?

The zero-energy universe hypothesis proposes that the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly canceled out by its negative energy in the form of gravity. Some physicists, such as Lawrence Krauss or Alexander Vilenkin, call this state "a universe from nothingness" but, in fact, the zero-energy universe model requires both matter field with positive energy and gravitational field with negative energy to exist.

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1 hour ago, SergUpstart said:

What do you think about zero-energy Universe model?

The zero-energy universe hypothesis proposes that the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly canceled out by its negative energy in the form of gravity. Some physicists, such as Lawrence Krauss or Alexander Vilenkin, call this state "a universe from nothingness" but, in fact, the zero-energy universe model requires both matter field with positive energy and gravitational field with negative energy to exist.

So what does this model explain or predict that other models fail to and do these predictions match with what we measure, are there even measurements or predictions that would make it possible to falsify this model?

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That wiki article poorly describes the zero energy model. It is simply taking kinetic energy of the particle and subtracting the potential field energy. Both energy densities are still positive.

Also that model requires pseudo tensors and only works well for Cartesian coordinates.

It does not imply gravity is negative mass

Edited by Mordred
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6 minutes ago, Mordred said:

That wiki article poorly describes the zero energy model. It is simply taking kinetic energy of the particle and subtracting the potential field energy. Both energy densities are still positive.

Also that model requires pseudo tensors and only works well for Cartesian coordinates.

It does not imply gravity is negative mass

So would you say that this model has evidence supporting it that other models don't have, or is this model just a different way of expressing particular formulas (aka, nothing changes just a different interpretation)?

Or are there specific moments/scenarios where using this model is easier or more accurate than other models?

Edited by Dagl1
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Simply a different interpretation that has viability but is often misunderstood until you dig into the mathematics..

It is largely based upon the Zero point energy of the quantum harmonic oscillator.

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On 12/1/2019 at 11:16 AM, SergUpstart said:

What do you think about zero-energy Universe model?

The zero-energy universe hypothesis proposes that the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly canceled out by its negative energy in the form of gravity. Some physicists, such as Lawrence Krauss or Alexander Vilenkin, call this state "a universe from nothingness" but, in fact, the zero-energy universe model requires both matter field with positive energy and gravitational field with negative energy to exist.

Not a lot since it implies some serious difficulties with Entropy.

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• 2 weeks later...

American physicists have shown that phonons that move against the background of a solid or an ideal liquid carry a small negative mass. To do this, the scientists considered the effective theory of the point particle and found corrections to the energy-momentum tensor of phonons. According to scientists, the predicted effect can already be confirmed with the help of Bose condensates or seismic waves. The paper is published in Physical Review Letters and is in the public domain, briefly reported by Physics.

Usually physicists believe that sound waves do not carry mass. Of course, waves carry momentum and energy, which, according to General relativity, are equivalent to a small amount of mass, but beyond this effect, nothing should be. At least, that's what the linear models of sound waves say, which agree well with the experiment.

However, last year, theoretical physicists Alberto Nicolis (Alberto Nicolis) and Riccardo Penco (Riccardo Penco) suddenly discovered that this is not the case. Using an effective theory for a point particle, scientists have shown that in superfluid helium at zero temperature, phonons-the quanta of sound vibrations-interact effectively with the gravitational field, and the strength of this interaction depends only on the energy of the quasiparticles and the equation of state of the liquid. Moreover, the effective mass of phonons turned out to be negative — in other words, sound waves deviate towards a weaker gravitational field.

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What does this have to do with anything under discussion?

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I suggest you look closer in the solid state case. One can assign a negative mass when compares to a larger mass value. That doesn't help you with your hypothesis.

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• 4 months later...

The us West Texas Intermediate (WTI) light crude futures contract for delivery in may ended the trading session on April 20 at minus \$37.63 per barrel, according to data from us exchange operator CME Group.

So the mass can also be negative. 