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 tensor for Dirac fields, and its dependence on connection

In the stress-energy tensor (SET) for free scalar and vector fields, any references to the connection $\Gamma^\lambda_{\mu\nu}$ in the kinetic terms appear to either be absent ($\nabla_\mu \phi = \...
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Interpretation of components of energy-momentum flux near a null surface

Let $k^a$ be the normal to a null surface and $l^a$ be the auxiliary null vector satisfying $l^a k_a=-1$ (see, for instance, the textbook A Relativist's Toolkit by Poisson). I wanted to understand ...
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Why not $\rho^{2}=T^{\mu\nu}T_{\mu\nu}$ as an effective mass density (squared ) in general relativity?

Why not $\rho^{2}=T^{\mu\nu}T_{\mu\nu}$ as an effective mass density (squared) in general relativity? It's covariant, and as far as I can tell is zero for any electromagnetic field tensor. \begin{...
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On the definition of Lagrangian

I have a question about "the definition of Lagrangian" in spacetime manifold. In general relativity, the energy-stress tensor and the vacuum energy stress tensor can be written as below: $$T_{\nu\mu}=...
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53 views

Position of indices in QFT

I have recently started studying quantum field theory from the book Quantum Field Theory and the Standard Model by Schwartz. In chapter 2 it is said that, contrary to GR, one can ignore the index ...
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95 views

Metric with Harmonic Coefficient and Stress-Energy Tensor in General Relativity

I have two question: Is there any possible implies or interest to use in general relativity a metric whose coefficients are harmonic functions? What is the meaning (physical) if the stress-energy ...
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OPE coefficents and commutation relations, and OPE with stress tensor

Basic question about conformal field theory: In a conformal field theory in $d\geq 3$ dimensions, what is the relation between commutation relations and OPE coefficients? In particular, because ...
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56 views

Transformation of quasi-primary field in CFT [closed]

As it is well known that in conformal field theory the energy-momentum tensor is a quasi-primary field, and its transformation law under conformal transformation $z\rightarrow w(z)$ is \begin{...
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52 views

Second derivative of the stress-energy tensor

Which physical meaning can have if the second derivative of stress-energy tensor is zero? In General Relativity or elsewhere.
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Correlator of energy-momentum tensor and OPE

In http://arxiv.org/abs/hep-th/9108028 Equation (2.22), the correlation function of then energy-momentum tensor with some primary fields is We can view this as sum over the OPE of the energy-...
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95 views

Energy-momentum tensor transformation [closed]

I've been trying to find how the energy-momentum tensor changes if we add a total derivative to the lagrangian: $$L\to L+\mathrm d_\mu X^\mu.\tag{1}$$ From the answer key: $$T^{\mu\nu}\to T^{\mu\nu}...
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Virasoro Algebra vs Witt Algebra

I'm reading some notes on CFT, and there's a strange topic that I find quite confusing. We define the Witt algebra to be the generators of conformal transformations on the complex plane. $l_n = -z^{...
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Flat space Solution of Einstein Field Equation

Does a trace-free energy-momentum tensor $T_{\mu}^{\mu} = 0$ ensure that the Einstein's field equations have a flat space solution?
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When is stress-energy tensor defined as variation of action with respect to metric conserved?

In General Relativity Einstein's equation implies that stress-energy tensor on its RHS is conserved (has vanishing divergence), due to the Bianchi identity. Considering variational principles leading ...
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Showing classical spin tensor is time independent for free particle

Reading through Weinberg's gravitation book, the following definition is given for the spin tensor (Pauli-Lubanski psuedovector): $$ S_\alpha = \frac{1}{2}\epsilon_{\alpha\beta\gamma\delta} J^{\beta\...
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23 views

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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88 views

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

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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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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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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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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68 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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1answer
54 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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201 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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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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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 $D_{...
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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 $$ T_{\mu\nu}=...
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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 -\frac{1}{2}\left(\...
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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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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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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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54 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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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} \mathbf{T}=(\...
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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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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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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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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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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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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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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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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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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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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 x^{\mu^{'}}=\Lambda^{\mu^{'}}_{\,\,\...
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“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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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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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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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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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 $\...
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Central charge in energy-momentum tensor OPE

I think that general point of view about central charge in books is considering OPE $T(z) T(w)$ for different field theories and finding that general expression for the most singular term is about to ...