BiGyElLoWhAt
Gold Member
- 1,637
- 138
Hi All. On Tuesday I have to present my research proposal for my undergrad research. I intend to model our solar system using general relativity and compare and contrast my results with observations. Attached is my paper that I had to submit to my adviser. He suggested that I talk about some methods that have been used before in my presentation, so I intend to add some talk about the schwartzchild and kerr solutions, and the general ideas behind finding them. However, the methods that I plan to use will be slightly different.
I have a few questions:
1) Any advice/ criticism is welcome.
2) Are there other major discrepancies between Newtons gravity and GR that can be easily outlined to an audience not versed in Relativity? (most of the people present won't have much experience with sr/gr)
3) Are there other solutions that would be worth mentioning? I feel like Schwartzchild is the simplest non-trivial, but I might be overlooking something or just not aware of it.
4) Feasibility - this gets more into the gist of the project:
Pretty much, my plan is to write my stress tensor in it's static frame and then lorentz transform it to whichever frame I will use, most likely the frame in which the sun has no translational motion, but if memory serves, the sun is rotating, so I will likely have that in my stress tensor. So basically 0 + diag{M/V,0,0,0} for each object that I include, and then lorentz transform that to the frame mentioned earlier.
As for solving, I am drawn toward Fourier solutions. We rotate periodically, so at least for the spatial coordinates, I feel like Fourier solutions would look nice and make physical sense. What do you think? The other option is difference equations, which I would just do on my computer.
In my tensor construction, what do you think I need to include? Obviously the sun and the planets. Earth's moon will be in there as well. Should I include the other moons, or would they have a negligible effect? The asteroid belt? etc. My goal is to be as accurate as possible without going overboard. I will likely try a few different things, but I would like some educated opinions just as a starting point.
Again, my paper is attached (this is not my presentation, but my paper submitted to my adviser to approve me presenting).
Thanks in advance.
I have a few questions:
1) Any advice/ criticism is welcome.
2) Are there other major discrepancies between Newtons gravity and GR that can be easily outlined to an audience not versed in Relativity? (most of the people present won't have much experience with sr/gr)
3) Are there other solutions that would be worth mentioning? I feel like Schwartzchild is the simplest non-trivial, but I might be overlooking something or just not aware of it.
4) Feasibility - this gets more into the gist of the project:
Pretty much, my plan is to write my stress tensor in it's static frame and then lorentz transform it to whichever frame I will use, most likely the frame in which the sun has no translational motion, but if memory serves, the sun is rotating, so I will likely have that in my stress tensor. So basically 0 + diag{M/V,0,0,0} for each object that I include, and then lorentz transform that to the frame mentioned earlier.
As for solving, I am drawn toward Fourier solutions. We rotate periodically, so at least for the spatial coordinates, I feel like Fourier solutions would look nice and make physical sense. What do you think? The other option is difference equations, which I would just do on my computer.
In my tensor construction, what do you think I need to include? Obviously the sun and the planets. Earth's moon will be in there as well. Should I include the other moons, or would they have a negligible effect? The asteroid belt? etc. My goal is to be as accurate as possible without going overboard. I will likely try a few different things, but I would like some educated opinions just as a starting point.
Again, my paper is attached (this is not my presentation, but my paper submitted to my adviser to approve me presenting).
Thanks in advance.