What is Energy-momentum tensor: Definition and 59 Discussions
The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields. This density and flux of energy and momentum are the sources of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity.
Electrodynamics force is f_i=F_{ik}j^k=F_{ik}\partial_j F^{jk}. I claim that the only way to obtain the Maxwell energy-momentum tensor T_i^j=-F_{ik}F^{jk}+\delta_i^jF_{kl}F^{kl}/4 is to write the force as a divergence: f_i=-\partial_jT_i^j.
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...
Homework Statement
In Minkowski space, we are given a scalar field \phi with action
S= \int d\Omega (\frac{-1}{2}\phi^{,a}\phi_{,a} - \frac{1}{2}m^2\phi^2)
We need to calculate the "translation-invariance" energy-momentum tensor:
T^a_b = \frac{\partial \mathcal{L}}{\partial \phi_{,a}}...
Homework Statement
1) Use conservation of Energy-Momentum Tensor to show that
\partial_{0}^{2}T^{00}=\partial_{m}\partial_{n}T^{mn}
Homework Equations
\partial_{\nu}T^{\mu\nu}=0
The Attempt at a Solution
\partial_{\nu}T^{\mu\nu}=0...
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?