Okay so I have:
Eqn1) Tij=\rhouiuj-phij = \rhouiuj-p(gij-uiuj)
Where Tij is the energy-momentum tensor, being approximated as a fluid with \rho as the energy density and p as the pressure in the medium.
My problem:
Eqn2) Trace(T) = Tii = gijTij = \rho-3p
My attempt:
Tr(T) = Tii...
Homework Statement
The problem is conveniently located here:
http://www.dur.ac.uk/resources/cpt/graduate/lectures/mscps.pdf
Problem no. 31. There's even a solution, here:
http://www.dur.ac.uk/resources/cpt/graduate/lectures/grsolns.pdf
However, I don't understand the solution...
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I'm studying General Relativity and facing several problems. We know that energy-momentum must be Lorentz invariant in locally inertial coordinates. I am not sure I understand this point clearly. What is the physics behind?
Hi all,
In Polchinski's string theory text he asserts (volume 1, section 3.4) that the trace of the energy-momentum tensor of a classically scale -invariant theory becomes proportional in the quantum theory to the beta function of the coupling, as a general point of QFT. This makes a kind of...
Hi,
I believe you can use the "energy-momentum tensor" to express the conservation of both energy and momentum for fields (\partial_{\mu} T^{\mu \nu} = 0). But I'm wondering: why's a tensor needed, specifically, to describe this conservation of energy and momentum for fields? For particles, I...
Hi
I have a small subtle problem with the sign of the energy-momentum tensor for a scalar field as derived by varying the metric (s.b.). I would appreciate very much if somebody could help me on my specific issue. Let me describe the problem in more detail:
I conform to the sign convention...
I was wondering if someone could clarify something that I read in a book (Nakahara's book on Geometry, Topology, Physics). In the section on the Einstein-Hilbert action, the author defines the energy-momentum tensor as
\delta S_M = \frac{1}{2} \int T^{\mu \nu} \delta g_{\mu \nu} \sqrt{- g} d^4...
Is it correct that the only way to have a theory of gravitation that fulfills the equivalence principle is to make use of a tensor as the source of gravity (and not a scalar or a vector, for example)? How can this be proven?