Maxwell's tensor: http://www.physicspages.com/2014/06/09/maxwell-stress-tensor/ Momentum in electromagnetic fields: http://www.physicspages.com/2014/06/13/mo

The stress-energy tensor allows us to express conservation of energy-momentum as $\frac{\partial T^{ab}}{\partial x^a} = 0$ This local conservation of energy-momentum is all we get in general relativity. As discussed in section 4.3, there is no such global law in curved spacetime. Feb 26, 2013 · We derive electromagnetic continuity equations and equations of motion for the macroscopic fields based on the material four-divergence of the traceless, symmetric total energy-momentum tensor. We identify contradictions between the macroscopic Maxwell equations and the continuum form of the conservation principles. that no improvements of the energy-momentum tensor are possible. It was shown in  that the traceless-ness of the stress-energy tensor follows in d = 2 from scale invariance 3 Another equivalent description of the conditions for scale vs. conformal invariance can be The linearized field equation is of course G = 8 GT, where G is given by (6.8) and T is the energy-momentum tensor, calculated to zeroth order in h. We do not include higher-order corrections to the energy-momentum tensor because the amount of energy and momentum must itself be small for the weak-field limit to apply. Einstein devised his energy-momentum tensor (fig. 1b) starting with the constraint tensor of the 1850's fluid mechanics (fig. 1a). Without enter in the build of these two tensors, the following points must be highlighted: In the constraint tensor (fig. 1a), the trace T 00, T 11, T 22, defines the isostatic pressure. where is the three-dimensional energy–momentum tensor and G the momentum density of the field in the medium. It is easy to show that equation ( 12 ) can be cast in this form. For example, to obtain the corresponding transformation for f e (equation ( 13 )), we first write Energy-Momentum Tensor . Incoherent Matter Case . One of the simplest energy-momentum tensors is the dust energy momentum tensor. This type of matter field consists of noninteracting incoherent matter. The matter field depends on one scalar quantity and one vector quantity. These two quantities are as follows:

## On the Trace Anomaly and the Energy-Momentum …

calcuIate the energy-momentum tensor of the Schwarzschild geometry. It turns out that it is possible to include the singular region (i.e. the spacelike line r = 0 with respect to Schwarzschild coordinates) in the spacetime which now no longer is a vacuum geometry, and to identify it with the support of the energy-momentum tensor. Conditions for Traceless Symmetric Improved Stress … 2003-2-13 · 26 Chapter 5 Conditions for Traceless Symmetric Improved Stress-Energy Tensors Any new candidate for a stress-energy tensor must (1) conserve, (2) define the same energy-momentum…

### The U.S. Department of Energy's Office of Scientific and Technical Information OSTI.GOV Journal Article: Energy-momentum tensor of the electromagnetic field

where is the three-dimensional energy–momentum tensor and G the momentum density of the field in the medium. It is easy to show that equation ( 12 ) can be cast in this form. For example, to obtain the corresponding transformation for f e (equation ( 13 )), we first write Energy-Momentum Tensor . Incoherent Matter Case . One of the simplest energy-momentum tensors is the dust energy momentum tensor. This type of matter field consists of noninteracting incoherent matter. The matter field depends on one scalar quantity and one vector quantity. These two quantities are as follows: the two point function of the energy momentum tensor hT (x)T (y)iand the necessary conditions required to satisfy the conservation equation for the energy momentum tensor are obtained. On S 2or H for a traceless energy momentum tensor these have simple solutions with only an undetermined overall scale for S2. Expressions which satisfy the Also, remember that "energy" is the same as "momentum in the time direction", and that "density" is the same as "flow in the time direction". Thus the top row of the stress-energy tensor keeps track of the density of energy --- that's T 00--- and the density of momentum in the x,y, and z directions --- those are T 01, T 02, and T 03 respectively. The quantity T is the so-called energy-momentum-stress tensor or in a shorter version the energy-momentum tensor4 or the stress-energy tensor. It is a rank-2 symmetric tensor encoding all the information about energy density, momentum density, stress, pressure . The ten components of this tensor have the following interpretation: stress-energy tensor T = 1 4ˇ F γF γ− 1 4 F γ Fγ (8) that is symmetric and traceless by construction just as in electromagnetism. We can also de ne the GEM angular momentum density tensor J γ =(X−C)T γ− X −C T γ; (9) where C :(˝;0) denote the coordinates of the ducial test observer at the center of the over the role of ˆin general relativity, viz. the mass-stress-energy-momentum density tensor T .1 Nevertheless, the non-vanishing of an energy tensor T at a point will turn out to be a necessary and su cient condition for this point to be occupied by matter.2 1For simplicity, I will often just speak of the ‘energy-momentum tensor’ or even