Gravity and all that:

[beecee]

I once crossed swords with a person who was obviously a "professional" of sorts [at least he seemed competent in maths] when I made a comment to another that gravity makes more gravity.

This is due to the property of nonlinearity of spacetime/gravity. I supported my claim with a link to the "Einstein online"site which at this time appears to be down.

His "reputation" though was eventually tarnished with his rather grandiose claim that he had disproved GR and later the recently three GW discoveries did not further validate GR.

Can someone give a more complete reasoning as to the question of gravity making more gravity, and the property of nonlinearity?.

 

On another matter, I was confronted rather forcefully [don't be too concerned, I'm a tough old bastard! ] when I made the comment that light/photons exert gravity, albeit by a very small amount: That of course is due to its momentum, which again is evident with the operation of light sails for interplanetary/stellar travel.

Further discussion or confirmation on that point is also welcome.

Here is that link and a short extract.............................

 

http://www.scienceforums.net/topic/107918-gravity-and-all-that/

 

The gravity of gravity An article by Markus Pössel Contents

1. Adding forces
2. The building blocks of Newtonian gravity
3. Linearity
4. The building blocks of electrodynamics
5. Goodbye to the building blocks: Energy as a source of gravity
6. General relativity: a theory with non-linear laws
7. Further Information

One reason why the physics of general relativity is much more difficult than that of Newton's theory of gravity or the theory of electrodynamicsis a property called non-linearity. In short, gravity can beget further gravity - where gravitational systems are concerned, the whole is not the sum of its parts.

Edited July 15, 2017 by beecee

[Mordred]

There is a formula one can use to show this.

 

Lets assume we are in the weak field Newton approximation.

 

[latex]g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}[/latex]

 

Now this formula is commonly used to describe a small perturbation a GW wave or any small non linear perturbation.

 

The linear portion is the Minkowskii tensor [latex]\eta[/latex] this is the Approximately Euclidean tensor. Which for weak gravity such as Earth is approximately accurate only if you ignore the directional density variation described by the perturbation tensor

 

When a GW hits the sum of the GW wave described by the perturbation tensor adds to the Minkowskii tensor giving the metric tensor on the LHS.

 

 

Now you know the Minkowskii tensor is a scalar uncharged field, with no inherent direction when you look at its ds^2 line element. However when you add the perturbation tensor this is where the non linear portions come into play. In essence the nonlinear perturbation tensor charges our Minkowskii tensor.

 

Now if you recall the above formula is used to describe gravity of planets,stars of non relativistic influence.

 

Hence the Newton approximation. A GW wave uses the identical formula above. The differences between a planet or a GW wave is reflected in the perturbation tensor which will not be identical in the two mentioned scenarios.

 

However both are describing how non linearity mass density curves the flat Euclidean Minkowskii tensor above.

 

(the perturbation tensor is far more complex in the GW case) but how two affect gravity is essentially the same. except for the additional degrees of freedom in the vector components.

 

The stress tensor for a GW wave will have more flux and vorticity in the stress tensor.

 

The same thing occurs with photons. Your photons affect are reflected in the perturbation tensor accorrdingly to the stress tensor components.

 

In essence you apply non linear fields to the perurbation tensor

 

[latex]h_{\mu\nu}=\eta_{\mu\nu}[/latex]

 

Applying the stress tensor to our non linear via

[latex] T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p \eta^{\mu\nu} [/latex]

 

Gives us our resulting perturbation tensor which we can further apply to the metric tensor. (regardless of if previously curved or not) ie approximately Euclidean or curved under [latex]g_{\mu\nu}[/latex] example the Scwartzchild approximation

 

[latex]g_{\mu\nu}=g_{\mu\nu}+h_{\mu\nu}[/latex]

 

Kind of reflects how handy tensors are lol awesome way to sort different vector symmetry translations.

 

In the last equation you have already previously defined the metric and in the last equation you are further perturbing it. Your field perturbation is reflected in the perturbation tensor or combination of perturbations ie polarities.

 

[latex]h_{\mu\nu}=h_+ +h_{\times}[/latex]

Edited July 16, 2017 by Mordred

[beecee]

Thanks for that truly in depth rundown Mordred.

I would guess that not too many lay people would know about the two facts you have given an explanation of, and the property of nonlinearity.

So perhaps the thread has done some good.

[Mordred]

Agreed most people seldom study the three classes of solutions under GR.

 

1) vacuum

2) Newton approximation

3) Scwartzchild metric.

 

When you realize that tidal forces are added via the perturbation tensor GR starts to make more sense.

 

Far too often they understand the Principle of equivalence which is the symmetric transforms described by Lorentz and thusly the Minkowskii metric tensor.

 

However they rarely understand tidal force under the perturbation tensor for the Principle of general covariants. Hence coincidently both gravity due to the curvature terms (anistropic) and GW waves are both tidal forces. Now that you know this. You know know the tensor used to describe tidal forces as being the perturbation tensor.

 

The tidal forces is also your deviations from parallel light paths. The Minkowskii tensor itself is strictly parallel paths.

 

Lol by analogy they read the beginning and end of a book but not what occurs in the middle stages.

 

Very similar to laymen knowledge. They know some basics. Hear about some final result and not understand what occurs in the steps to arrive from beginning to end result.

 

Just a side note, that knowledge also allows me to spot personal models trying to solve expansion etc. They usually only post the Minkowsii tensor relations which don't include the curvature terms. That and they get the time dependant and time independant metrics mixed up.

 

PS by the way it was a pleasure just needing to refer to the tensors and knowing your already familiar with them made things far easier and pleasant lol. +1.

Edited July 17, 2017 by Mordred