The discussion centers on the complexities of the stress-energy tensor in General Relativity (GR), particularly regarding gravitational fields. Participants clarify that the stress-energy tensor for gravitational fields is often considered zero due to the ability to transform the metric to zero at a point, which implies no local measure of energy-momentum for gravity. They reference the Einstein field equations, emphasizing that the covariant divergence of the stress-energy tensor is zero, indicating a conservation law that does not account for gravitational energy. Key texts mentioned include "Gravitation" by Misner, Thorne, and Wheeler (MTW) and a paper by D. Lynden-Bell and J. Katz on gravitational field energy density.
PREREQUISITESStudents and researchers in theoretical physics, particularly those focusing on General Relativity, gravitational theory, and the mathematical foundations of energy-momentum in curved spacetime.
You certainly have made a mistake. Can you reproduce your calculations in here?Jonathan Scott said:Sorry, I have to admit I don't recall the specific details, but a few years ago when I added up the total LL field energy with the "matter energy" of the source, the total wasn't equal to the rest mass minus the potential energy. I thought perhaps I'd made a mistake in calculating the LL energy density and asked a friend of mine (a professor of physics at Southampton University) to check it; he agreed with my conclusion and found it puzzling, but didn't have time to investigate any further. In contrast, the density given by Lynden-Bell matches up exactly with the semi-Newtonian model.
It's quite likely that I made a mistake, but that was some time ago and it's unlikely I kept notes for something that didn't work; I certainly don't have them in my file of interesting notes, although I may be able to find some of my correspondence on the subject. I seem to remember the effective field energy density being 7/2 times the square of the Newtonian field instead of 1/2, but that may have been when using a non-equivalent coordinate system.samalkhaiat said:You certainly have made a mistake. Can you reproduce your calculations in here?
samalkhaiat said:In this case, I suggest you postpone stepping into this treacherous and controversial territory until you finished one of the good textbooks on GR.
Its good to be in this forum and see people like you saying such a sentence. Because if I were to only look at the physics students around myself, I would do a really bad mistake in overestimating my level of knowledge!samalkhaiat said:No, you don't. I don't regard myself as "expert". I just know few things.
I can only suggest what I believe the golden rule in learning: Read the book that you understand and think it is nice. A book that one finds "good and nice" might not be as "good and nice" for others.Shyan said:Actually I have some doubts here. Which book should I read? Ryder? Zee? Weinberg? Straumann? Carroll? MTW(just kidding!:D)?
I have the problem that since I know things about GR, I become bored on some sections. Also I want a book that covers advanced and exciting topics in a mathematically serious way. So I need a book that, in addition to being good, should be a bit advanced too. Can you suggest one?