A rank-2 tensor in relativity, which expresses the flux of energy-momentum along timelike and spacelike axes. Also known as the energy-momentum tensor. In the Einstein field equations, it is the source of gravitational fields.

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Stress-Energy Content

I think that the Einstein Field Equation relates the pseudo metric to the the distribution of matter-energy as represented by the stress-energy tensor. Are the stress entries in the stress-energy ...
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81 views

Interpreting $Q_i=\partial_{\nu}T^{i \nu}$ from dust

I am working on Sean Carroll's problem 1.8 If $\partial_\nu T^{\mu \nu} = Q^\mu$, what physically does the spatial vector $Q^i$ represent? Use the dust energy momentum tensor to make your case. ...
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24 views

Scale invariance and stress energy tensor

I have seen in a paper [1] that in a quantum field theory scale invariance takes place provided the stress energy tensor is traceless. How this is true? References: "INFINITE CONFORMAL SYMMETRY IN ...
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77 views

What is more fundamental: Geometry and Topology or physical matter? [closed]

Since, there is always an interplay between gravity and the fabric of spacetime. I wonder which is more fundamental: Geometry and Topology or physical matter?
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7 views

Warping function for torsion of non-circular prism

I have a few questions regarding the case of torsion of a prism, as encountered in continuum mechanics. Specifically, a prism (which can be a cylinder, a rectangular prism, elliptical prism, etc.) has ...
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48 views

Electromagnetism theory and complex scalar field

I've got the following problem for classical field theory lecture: Find equations of motion (equations of field?), canonical and symmetrical tensor of energy-momentum in electromagnetic field ...
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393 views

Pressure and density using a general Lagrangian

Given a lagrangian of a form: \begin{equation}\mathcal{L}=f(\phi,\partial_{\mu}\phi\partial^{\mu}\phi)\end{equation} where $f$ is a function, I need to derive pressure and density in a FLRW universe ...
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49 views

What are the vacuum Einstein's equations? [closed]

I read on Wikipedia that if the Stress-Energy Tensor is set to zero in General Relativity's Field Equation that it makes the Vacuum Equations. What are these equations, and how are they used?
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114 views

Maxwell Stress Tensor at material boundaries

I am trying to grasp the meaning of the Maxwell Stress tensor $T_i^j$ at material boundaries. Concretely, I am trying to calculate the force between two waveguides. The results are given in an article ...
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181 views

Why does matter curve space time? [duplicate]

I am under the impression that Einstein never explains in his General Theory of Relativity, why matter curves spacetime; could explanations please be given?
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1answer
590 views

What does Weinberg–Witten theorem want to express?

Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin $j > 1/2$ cannot carry a Lorentz-covariant current, while massless particles with spin $j > 1$ ...
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2answers
100 views

Does metric signature affect the stress energy tensor?

If one were to derive the stress-energy tensor for a metric with $(+,-,-,-)$ signature would it be different from the stress-energy tensor derived from the same metric but with $(-,+,+,+)$ signature?
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26 views

Inequivalent matter actions with the same stress-energy tensor in general relativity

In general relativity, suppose as usual that we have the following action for the matter fields \begin{equation} S_{\mathrm{matter}} = \int_M d^4 x \sqrt{-g} L_{\mathrm{matter}} , \end{equation} ...
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17 views

An expression for stress power

I have seen it written that for a continuum undergoing deformation, if we ignore body forces and heat transfer, the work done is equal to stress power: $\cfrac{dW}{dt}=\sigma_{ij}D_{ij}$, where ...
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1answer
174 views

Why can we not choose the stress tensor in a CFT to be identically symmetric?

The stress tensor for a conformal field theory (or any quantum field theory) can be derived from the action $S$ by the functional derivative $$T^{\mu \nu} ~=~ -\frac{2}{\sqrt{|g|}}\frac{\delta ...
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1answer
86 views

The dimension of the energy-momentum tensor and the Einstein-Hilbert action

I have been thinking recently what will happen if one uses the energy momentum tensor of the Dirac field as a source in the Einstein Field equations. It is well known that in this case $$ ...
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2answers
68 views

What is the purpose of the Maxwell Stress Tensor?

In the calculation of the forces acting on a charge/current distribution, one arrives at the Maxwell stress tensor: $$\sigma_{ij}=\epsilon_0 E_iE_j + \frac{1}{\mu_0} B_iB_j ...
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382 views

Is it possible that Cauchy stress be asymmetric?

According to conservation of linear momentum and angular momentum, one can derive that Cauchy stress tensor is symmetric and hence has only 6 independent components. Is it possible that, when breaking ...
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1answer
818 views

Derivation of Maxwell stress tensor from EM Lagrangian

From Noether's theorem applied to fields we can get the general expression for the stress-energy-momentum tensor for some fields: $$T^{\mu}_{\;\nu} = \sum_{i} \left(\frac{\partial ...
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1answer
75 views

Understanding Vaidya metric and pure radiation stress-energy tensor

I am following Vaidya metric and how it is related to pure radiation from Wikipedia. But when it reaches the line where stress-energy tensor is equated to product of two four-vectors, I cannot follow ...
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67 views

What is the explicit form of $\tau^{\alpha\beta}$ in the linearized Einstein field equations $\Box h^{\alpha\beta}=-16\pi\tau^{\alpha\beta}$?

If we let $h^{\alpha\beta}=\eta^{\alpha\beta}-g^{\alpha\beta}\sqrt{|det(g)|}$ then, according to wikipedia, the Einstein Field Equations become $$\Box h^{\alpha\beta}=-16\pi\tau^{\alpha\beta},$$ where ...
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487 views

What kind of object is the Landau--Lifshitz pseudotensor?

I understand that it's called a pseudotensor because it's not a tensor. Wikipedia says most pseudotensors are sections of jet bundles, which are perfectly valid objects in GR. ...
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124 views

Is every solution of Einstein field equations unique?

Einstein's equation is $$8 \pi T_{ab} = G_{ab},$$ where the left side contains the stress-energy tensor and the right side contains the Einstein tensor. Is there exactly one unique stress-energy ...
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43 views

Evaluating the components of Maxwell's stress tensor

I was going through the Maxwell's stress tensor section of Introduction to Electrodynamics by Griffiths. In the example 8.2(screenshot below), I fail to understand how the equation 8.23 (in the ...
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52 views

On the isotropy of materials

I am working on honeycomb structures and first of all I would like to understand whether it is isotropic or not, and, if the latter holds, which kind of anisotropy does it have? How to do it? I don't ...
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1answer
238 views

Why does Weyl invariance imply a traceless energy-momentum tensor?

I've begun to self-study String Theory from Polchinski and Becker, Becker and Schwarz. I don't see why the fact that the Polyakov action is invariant under Weyl transformations is related to the ...
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86 views

Relation of conformal symmetry and traceless energy momentum tensor

In usual string theory, or conformal field theory textbook, they states traceless energy momentum tensor $T_{a}^{\phantom{a}a}=0$ implies (Here energy momentum tensor is usual one which is symmetric ...
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207 views

Time dilation as an effect of energy density

Has any relation been observed or postulated to exist between the energy-density (or the surrounding space) of an object and time dilation? i.e. Higher energy density==>Slower rate of time?
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48 views

In General relativity, what is the meaning of flow of $x$ momentum in $x$ direction or pressure in $x$ direction? [duplicate]

I found this interesting paper on Arxiv devoted to explaining Einstein's field equations in simple English. The author, JC Baez, does this by considering a group of small spherical balls in ...
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55 views

Einstein's Equations [closed]

Can one please explain tensors, specifically stress energy tensors and its application in Einstein's Equations? I am a beginner cosmology learner and want to know the meaning and significance of ...
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40 views

Photon Gas Stress-Energy Tensor

In standard texts it is typically discussed how one can obtain the stress energy tensor of a perfect fluid, in both coordinate-dependent and coordinate independent forms: \begin{equation} ...
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55 views

What is the affection of stress tensor of spacetime by the energy/mass density moment of a photon? [closed]

First of all what kind of moment exhibits the photon under its propagation to spacetime continium -quadrupole,dipole or monopole! Please, explain me- why. Do Give some arguements! When it propagetes ...
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41 views

Imaginary part of the stress-energy tensor

I just encountered in an article of D. G. Boulware ("Quantum Field Theory in Schwarzschild and Rindler Spaces", Phys. Rev. D 11, 1404, 1975, in the last paragraph of the Introduction) the statement ...
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452 views

Lorentz invariance of the Minkowski metric

As far as I understand, one requires that in order for the scalar product between two vectors to be invariant under Lorentz transformations $x^{\mu}\rightarrow ...
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Non-locality of gravitational energy

Gravitational energy is non-local which is essentially because of the equivalence principle. The equivalence principle says that you can always transform your frame so that you feel like in a ...
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36 views

Electromagnetism and Energy-Momentum Tensor [closed]

I'll begin with the question: A plane electromagnetic wave propagating in the z-direction has fields $E = E_0 \hat{x}cos[\omega(t-z)], B = E_0 \hat{y}cos[\omega(t-z)]$. Find all components of the ...
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42 views

Can nonconserved energy in GR be thought of as going into gravitational field energy?

One of the most striking features of GR is that energy is not conserved. Carroll's GR text has an interesting statement about this: Clearly, in an expanding universe... the background is changing ...
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287 views

What exactly is $T_{\mu\nu}$?

Continuous matter is described in special relativity by the matter tensor which is the so-called stress-energy-momentum tensor. I am finding a difficulty understanding how a tensorial tool ...
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1answer
661 views

Lagrangian definition of stress energy tensor of matter

Can anyone explain why $$T_{\mu \nu} = \frac{2}{\sqrt{-g}} \frac{\delta \mathcal{L}_M}{\delta g^{\mu \nu}} ,$$ other than justifying it from the Einstein field equations?
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46 views

How is momentum conserved in this electromagnetic scattering?

It is well known that verifying momentum and energy conservation in the presence of electromagnetic fields requires care as the fields themselves carry energy and momentum (see Griffiths chapter 8 for ...
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141 views

Einstein field equations and SEM tensor + Alcubierre

I wonder how I can find, using the Einstein field equations, the SEM tensor in a region of space with a function $k(x,y,x)$ that describes the curvature of space in that region at a moment (so it is ...
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31 views

Special conformal transformation of stress-energy

Consider a 2d CFT, e.g. a single bosonic degree of freedom. The $TT$ OPE is $$ T(w) T(z) = \frac{c/2}{(z-w)^4} + \frac{2 T(w)}{(z-w)^2} + \frac{\partial T(w)}{z-w} + \text{regular terms}. $$ Does ...
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76 views

Dimensional inconsistency in first law of black hole thermodynamics

The first law of black hole mechanics (let's simplify by considering a uncharged and non-rotating black hole) can be written as $$\delta M = T \delta S$$ If I use the definition of Hawking ...
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42 views

“Simple” Variation of the gravity action with boundary

I'm concerned with the derivation of the quasi-local stress tensor (getting from eqn 2.4 to eqn 2.6 in this paper: http://arxiv.org/abs/hep-th/0508218). As is the case with all the references I have ...
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204 views

What is gravitational energy in general relativity?

In GR the curvature of spacetime "is gravity". This curvature is expressed via the Riemann tensor (or the Ricci tensor + Ricci scalar). The curvature is connected via the Einstein Field Equations with ...
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44 views

What is the property which flows as described by the stress energy tensor in GR?

I found the following definitions: The stress–energy tensor (sometimes stress–energy–momentum tensor or energy–momentum tensor) is a tensor quantity in physics that describes the density and flux of ...
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162 views

Pass to globally conserved currents from locally conserved currents in curved spacetime

Let us begin with a Lagrangian of the form $$\mathscr L= \frac 12 \sqrt{-g}g^{\mu\nu}\partial_\mu\phi(x)\partial_\nu\phi(x)+\mathscr L_g,$$ where $$\mathscr L_g=\frac 1{16\pi k}\sqrt{-g}R.$$ ...
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59 views

Einstein tensor as a conserved current?

As is well-known, the ``traditional" conserved quantities (energy, momentum...) are Noether currents whose conservation depends on the existence of various Killing fields in Minkowski space. In ...
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Stuck with physics tensile strength problem

So this was a question in my exam. I am not asking for the solution rather some help at a step. A glass spherical shell of radius $R$ has a point source of monochromatic light of wavelength ...