Einstein's Field Equations and Poisson's Equation

[Mueiz]

Excellent copying and pasting, but that wasn't the exercise. The exercise was to find the Laplacian of the potential inside a spherical mass, not outside. The potential inside a spherical mass is not -((G M)/r). See the link which I gave above in post 51:

http://en.wikipedia.org/wiki/Gravitational_potential#Spherical_symmetry

Mueiz, the gravitational potential inside a spherical mass is first-semester freshman physics material. If you don't know that, then you have no business trying to learn the EFE. I applaud your ambition, but you need to go back and learn basic Newtonian physics first. I mean, if you don't even know freshman physics nor differential equations then you are simply not equipped to understand the proof that you are asking for. We can post it (it is easy enough to find on the internet) but you won't be able to understand it.

Anyway, please complete the exercise and post your results and then we will proceed from there. Hopefully the exercise itself will be a valuable learning experience and will help prepare you for the proof.

There is no proof in this link to the formula.. what is there is only that he is using the formula
to recover the density.
Those who do not know what the meaning of proof is, and think that to find an equation in the the Holy wikipeadia without proof is a proof need not only go back and learn basic physics but ask themselves whether they are able to learn physics or not.

 

[Mueiz]

Excellent copying and pasting, but that wasn't the exercise. The exercise was to find the Laplacian of the potential inside a spherical mass, not outside. .

I will leave you reply to yourself (in your post#25)

Please do the exercise I suggested above. Start with the known gravitational potential outside of a point mass and then calculate the Laplacian and see what you get..

!
This is enough and I prefer to stop here.
But truly I often find your posts very beneficial like your first post in this thread and many others, but sometimes you seem to have no aim except for rejecting my arguments.

 

[Born2bwire]

http://farside.ph.utexas.edu/teaching/em/lectures/node31.html

 

[Dale]

I will leave you reply to yourself (in your post#25)

Yes, I already solved the exercise from post 25 and posted the result a long time ago. I was referring to the new exercise I suggested in post 51 which you have not solved nor posted. Please do so, if you desire to learn about Poisson's equation and Newtonian gravity.

But truly I often find your posts very beneficial like your first post in this thread and many others, but sometimes you seem to have no aim except for rejecting my arguments.

Only when your arguments are in conflict with known science.

 

[Dale]

what is there is only that he is using the formula
to recover the density.

Feel free to look elsewhere for the formula for the potential inside a uniform sphere. It is well known. Just cite your source, and then post your work on the exercise.

 

[Mueiz]

DaleSpam is right ..I apologize for Criticize his position falsely ... but his involving the case of the point mass and outside application of Poission Equation in a question related to using Poission equation as a model was not suitable ..Poission Equation is the Lanlacian of the potential (which is also equal dg/dr at far points from the source)
What is written in wikipeadia is imcomplete .because there should be a proof that begin in
from lablacian of ((4/3)G*pi*r^3)/r) to end at 4*pi*G*density.
I apologize for the second time for any bad word against him and thank him for correcting me

 

[Dale]

DaleSpam is right ..I apologize for Criticize his position falsely

Apology accepted, and I will try to avoid the unnecessary side comments in the future.

If you have further questions don't hesitate, and I would still recommend the exercise calculating the Laplacian inside a uniform spherical mass.

 

[Mueiz]

Apology accepted, and I will try to avoid the unnecessary side comments in the future.

If you have further questions don't hesitate, and I would still recommend the exercise calculating the Laplacian inside a uniform spherical mass.

No nead for exersise I think it is better for me to open a new thread concerning zero gravitational field where i am save from complicated mathemaics and exeperimental evidences:
In fact there is much to be learned from the relation between Poissin's Equation and einstein Field Equation even the statement of Einstein " Poisson Equation is used as a model to Field Equation '' nead futher discussion. it is a v good example how to get some information from the old theory to build new one.

 

[Dale]

In fact there is much to be learned from the relation between Poissin's Equation and einstein Field Equation even the statement of Einstein " Poisson Equation is used as a model to Field Equation '' nead futher discussion. it is a v good example how to get some information from the old theory to build new one.

It is good not just for understanding gravity but for also understanding science in general. By the time Einstein got around to GR Newtonian gravity had been around for a long time and there was a lot of experimental evidence supporting it. One thing that GR absolutely had to do was to reduce to Newtonian gravity in the appropriate limit. The same was true with Quantum Mechanics, it had to reduce to classical mechanics in the appropriate limit, and the same will be true with any future breakthrough theory, it must reduce to today's experimentally confirmed physics in the right limit.

 

[atyy]

An interesting discussion about guessing general relativity from Newtonian gravity is found on p 24 of http://arxiv.org/abs/gr-qc/0506065

 

[Mueiz]

Yes this is an interesting discussion ... but I want briefly and clearly :
1/ How to use PE to get information about EFE
2/ Reply to the criticisms that PE is Newtonian theory so not correct ..then is it correct to use it as a model for the desaired field equation ?
This is what i want (logic) but not the history of failure and success of einstein in his way to the Field Equation ,because it is not always true that the way theoreis is discovered is the best and clearest.
Henri poincare says: It is by logic we prove, but by intuition that we discover.