Stress-energy tensor

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	Stress-energy tensor - Wikipedia, the free encyclopedia
		Warning: In solid state physics and fluid mechanics, the stress tensor is defined to be the spatial components of the stress-energy tensor in the comoving frame of reference.
		The stress-energy tensor (sometimes stress-energy-momentum tensor) is a tensor quantity in physics.
		In General Relativity, the stress tensor is studied in the context of the Einstein field equations which are often written as
	en.wikipedia.org /wiki/Stress-energy_tensor (866 words)

	Talk:Stress-energy tensor - Wikipedia, the free encyclopedia
		I think this article should link to a new article on conservation laws in general relativity, in which it should be stressed that the divergence law for the stress-energy tensor does not have quite the interpretation expected from flat spacetime.
		I added some stuff, but there really ought to be a separate article on plain old stress tensors as opposed to relativistic stress-energy tensors, as I know this is a pretty important subject in engineering, and the relativity stuff is completely irrelevant in that context.
		Another point is that the stress-energy tensor plays a role in other metric theories of gravitation besides general relativity, so strictly speaking, I think this article really belongs in the category of things dealing with physical interpretation of Lorentzian manifolds.
	en.wikipedia.org /wiki/Talk:Stress-energy_tensor (410 words)

	Hamiltonians and the stress energy tensor
		Re: Hamiltonians and the stress energy tensor -- Sauron 3/17/03 (
		Re: Hamiltonians and the stress energy tensor -- Sauron 3/14/03 (
		Re: Hamiltonians and the stress energy tensor -- Sauron 3/16/03 (
	superstringtheory.com /forum/relboard/messages16/127.html (193 words)

	gravity.htm
		The stress- energy tensor results from a description, extremely accurate to be sure, of the universe in terms of the force in which the latter half of the nineteenth and the first half of the twentieth centuries were engulfed.
		Pauli's earlier energy-momentum tensor and the stress-energy tensor of more recent authors such as Zatskis are composed of a gravitational part and an electrodynamic part; this is most of what is needed and it works except that it does not predict photon decay or the red shift.
		Momentum and Energy which are returned to the space-time continuum through photon decay began in the first place by removing that momentum and energy from the place where they began, usually as an electron snapping from one energy to another in fluorescence (whether originated by thermal, photon or electron energy does not matter).
	members.chello.nl /~n.benschop/gravity.htm (2368 words)

	AZCompuguy - ScottoBobScotto - Subspace Technology
		More specifically, it is defined by the distribution of mass and energy which is mathematically defined by what is known as the stress-energy tensor of local energy distributions.
		Once the second layer is activated, the total energy of the warp field is _divided_ among the two stages of the tensor, and thus among the two layers of the subspace field.
		Where E is the energy of the layer (and thus the energy of the ship) and P_0 and E_0 are a power level and an energy level intrinsic to the model.
	www.azcompuguy.com /subspace.htm (15696 words)

	ScienceDaily: General relativity
		In special relativity, energy and momentum are joined in the four-momentum and the stress-energy tensors.
		Tensor calculus permits a manifold as mapped with a coordinate system to be equipped with a metric tensor of spacetime which describes the incremental (spacetime) intervals between coordinates from which both the geodesic equations of motion and the curvature tensor of the spacetime can be ascertained.
		Dark energy: An unobserved energy that is spread throughout the universe.
	www.sciencedaily.com /encyclopedia/general_relativity (5243 words)

	Stress
		To be exact, the stress at a point may be determined by taking the limit of the load being carried by a particular cross section, divided by that cross section, as the area of the cross section aproaches zero.
		In general the stress may vary from point to point, but for simple cases, such as circular cylinders with pure axial loading, the stress is constant and equal to the cross-sectional area divided by the applied load.
		Stress (roughly the opposite of relaxation) is a medical term for a wide range of strong external stimuli, both physiological and psychological, which can cause a physiological response called the general adaptation syndrome, first recognised in 1956 by Hans Selye.
	www.websters-online-dictionary.com /definition/english/st/stress.html (4318 words)

	research interests
		Method to compute the stress-energy tensor for the massless spin 1/2 field in a general static spherically symmetric spacetime, with Peter B. Groves, and Paul R. Anderson, Phys.Rev. D66, 124017 (2002).
		Stress-energy tensor for massless spin-1/2 in static black hole spacetimes, with William H. Hirsch, Benedikt Obermayer, Paul R. Anderson, and Peter B. Groves, Phys.Rev.Lett.
		The equations of G.R. are solved classically, with the classical stress-energy-momentum tensor replaced with the quantum mechanical average value.
	www.wfu.edu /~ecarlson/semiclassical.html (473 words)

	From Laue's stress-energy tensor to Maxwell's Equations \ and the implications for Einstein's GTR.
		From Laue's stress-energy tensor to Maxwell's Equations \ and the implications for Einstein's GTR.
		The stress energy tensor has to have two basic properties, it must be symmetric and it's divergence must be zero ([8], p.
		The electromagnetic system can be given a stress energy tensor in terms of the charge density current and the electric potential, as first done by Gustav Mie in 1912 ([4], p.
	home.tiscali.nl /physis/deHaasPapers/MPIRT05/deHaasMPIRT.html (2200 words)

	5.2 Stress-energy bi-tensor operator and noise kernel
		From the viewpoint of the stress tensor, the separation of points is an artificial construct, so when promoting the classical field to a quantum one, neither point should be favored.
		One of the most interesting and surprising results to come out of the investigations of the quantum stress tensor undertaken in the 1970s was the discovery of the trace anomaly [61, 84].
		The fundamental problem of defining a quantum operator for the stress tensor is immediately visible: The field operator appears quadratically.
	relativity.livingreviews.org /Articles/lrr-2004-3/articlesu8.html (1395 words)

	ipedia.com: Stress-energy tensor Article
		The stress-energy tensor is a tensor quantity in general relativity.
		This tensor is the Noether current associated with spacetime translations.
		There is in fact no way to define a global energy-momentum vector in a general curved spacetime.
	www.ipedia.com /stress_energy_tensor.html (164 words)

	5 Noise Kernel and Point-Separation
		Similar to what was done for the stress-energy tensor it is desirable to relate the noise kernel defined at separated points to the Green function of a quantum field.
		When we refer to, say, the fluctuations of energy density in ordinary (point-wise) quantum field theory, we are in actuality asking such a question.
		Thus, for comparison with ordinary phenomena at low energy we need to find a reasonable prescription for obtaining a finite quantity of the noise kernel in the limit of ordinary (point-defined) quantum field theory.
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2004-3/articlese5.html (751 words)

	stress.energy
		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.
		But it's only in general relativity where the stress-energy tensor is sitting proudly on the right side of an equation, telling spacetime how to curve.
		The 00-component is the thermal energy density and the ii-components are the pressure (one assumes an isotropic pressure for a ideal fluid).
	math.ucr.edu /home/baez/gr/old/stress.energy.html (1017 words)

	6.2 Sources of matter
		are the specific internal energy (per unit mass), pressure, rest mass density and four-velocity of the fluid.
		The corresponding energy and momentum conservation equations for the internal energy formulation of Section 6.2.4
		A few known examples include the admittance of expansion shocks, negative internal energies in kinematically dominated flows, the ‘carbuncle’ effect in high Mach number bow shocks, kinked Mach stems, and odd/even decoupling in mesh-aligned shocks [135].
	relativity.livingreviews.org /Articles/lrr-2001-2/articlesu16.html (913 words)

	YilmazAlley
		In particular, the stress-energy tensor they describe as that of Yilmaz's theory is in fact the standard stress-energy tensor of GR, obtained for example by varying the metric in the Lagrangian.
		On the other hand, the "Bianchi identity" for the stress-energy tensor, equation (**) above, is in fact identically satisfied by for any generally covariant matter system, as long as the matter obeys its own equations of motion.
		If the non-covariant divergence of the matter > stress-energy tensor had to vanish, then in the Newtonian limit there > could be no exchange of energy between kinetic and gravitational > potential forms.
	math.ucr.edu /home/baez/PUB/YilmazAlley (11204 words)

	culture data repository VBHT16: The Einstein Field Equations, Part 1
		If energy and momentum are to be locally conserved then there must be a restriction placed on the possible forms of stress-energy tensor, because that tensor determines the way that energy and momentum are flowing around in spacetime; in the jargon we say that the divergence of the stress-energy tensor must be zero.
		The field equations thus say that the Einstein tensor is proportional to the stress-energy tensor.
		Now, in relativity mass and energy are more or less the same thing, and the energy and momentum are related to each other in the same way as time and space are (as described in the discussion of symmetries and conservation laws).
	www.culturelist.org /cdr/article.cfm?id=24 (736 words)

	A renewed theory of electrodynamics in the framework of a Dirac-ether.
		This stress-energy tensor in fact can be related to the Dirac's new theory of electron.
		This experimental definition was accompanied by a mathematical one in the form of the stress tensor of a space with an electromagnetic field in it.
		So in the case of electrodynamics, energy as a particle travelling from A to B was out of the question and only a medium, called an ether, could explain the true mechanism of electric action ([2], p.
	home.tiscali.nl /physis/deHaasPapers/PIRTpaper/deHaasPIRT.html (6516 words)

	Mass Tensor
		T is sometimes referred to as the material energy tensor [1], as well as the energy-momentum tensor or the stress-energy tensor.
		to be proportional to the as the mass tensor of dust.
		Since the equation of continuity must be a tensor equation it follows that the complete mathematical representation of mass is a tensor of rank 2.
	www.geocities.com /physics_world/sr/mass_tensor.htm (325 words)

	My Research (Information about Casimir Effect)
		is the finite temperature vacuum expectation of stress tensor at a distance a.
		The stress tensor for the electromagnetic case is given by
		According to QED, the total vacuum expectation of zero point energy is infinite when summed over all the possible photon modes.
	www.pas.rochester.edu /~yildirim/research.htm (273 words)

	Stress-Energy-Momentum Tensors (ResearchIndex)
		The stress-energy-momentum tensor # that we construct is defined using the (multi)momentum map associated to the spacetime di#eomorphism group.
		Abstract: We present a new method of constructing a stress-energy-momentum tensor for a classical field theory based on covariance considerations and Noether theory.
		The tensor # is uniquely determined as well as gauge-covariant, and depends only upon the divergence equivalence class of the Lagrangian.
	citeseer.ist.psu.edu /603636.html (192 words)

	Re: Can the measured mass of an isolated system change
		Stress Energy Tensor, and instead of a single number it's a 4x4 matrix of numbers.
		So the answer to your question is that if there are electric or magnetic fields, the energy in those fields ends up in the Stress Energy Tensor, which will then determine the gravitational forces.
		The stress energy tensor takes into account energy and momentum, and photons have both.
	www.madsci.org /posts/archives/2004-09/1095342484.Ph.r.html (246 words)

	Re: Stress-energy tensor
		The energy-momentum tensor defined by the conformally coupled Lagrangian is often-times called an "improved energy momentum tensor".
		Basically, if you have a field which carries some "spin", (e.g., spinor, vector, tensor fields) you can expect trouble with the symmetry of the Noether expression for the energy momentum tensor.
		In all examples that I know of, the (conformally) improved tensor can also be obtained by adding terms with identically vanishing divergence to the traditional, Noether's first theorem formula.
	www.lns.cornell.edu /spr/1999-08/msg0017424.html (700 words)

	1 Overview
		On the theoretical issues, stochastic gravity is the necessary foundation to investigate the validity of semiclassical gravity and the viability of inflationary cosmology based on the appearance and sustenance of a vacuum energy-dominated phase.
		It is also a useful beachhead supported by well-established low energy (sub-Planckian) physics to explore the connection with high energy (Planckian) physics in the realm of quantum gravity.
		The mathematical properties of this quantity and its physical content in relation to the behavior of fluctuations of quantum fields in curved spacetimes are the central issues of this new theory.
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2004-3/articlese1.html (632 words)

	Stress Energy Tensor
		The stress energy tensor can be broken up into fluid (f) contributions and seed (s) contributions (see e.g.
		The latter is distinguished by the fact that the net effect can be viewed as a perturbation to the background.
		The fluctuations can be decomposed into the normal modes of §IIC as
	background.uchicago.edu /~whu/tamm/webversion/node16.html (51 words)

	Citebase - The gravitoelectromagnetic stress-energy tensor
		Authors: Mashhoon, B. McClune, J. Quevedo, H. We study the pseudo-local gravitoelectromagnetic stress-energy tensor for an arbitrary gravitational field within the framework of general relativity.
		Inspired by classical work of Bel and Robinson, a natural purely algebraic construction of super-energy tensors for arbitrary fields is presented, having good mathematical and physical properties.
		These tensors have good mathematical and physical properties, and they can be used in any theory having as basic arena an n-dimensional manifold with a metric of Lorentzian signature.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/9805093 (1025 words)

	Citebase - The stress-energy tensor for trans-Planckian cosmology
		This stress-energy tensor is then used to discuss both the equation of state of trans-Planckian modes in cosmology and the magnitude of their backreaction during inflation.
		This article presents the derivation of the stress-energy tensor of a free scalar field with a general non-linear dispersion relation in curved spacetime.
		It is suggested, by using a covariant lagrangian formalism to estimate the equation of state w = p/ρ, that stringy dark energy predicts w < -1, a negative pressure larger in magnitude than that for a cosmological constant or quintessence.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:hep-th/0109128 (1310 words)

	3.1 Semiclassical gravity
		we explicitly indicate that the stress-energy tensor is a functional of the metric
		The classical stress-energy tensor is obtained by functional derivation of this action in the usual way,
		Note that both the stress tensor and the quantum state are functionals of the metric, hence the notation.
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2004-3/articlesu2.html (821 words)

	4tensor.nb
		These are the Maxwell stress tensor, \ the Poynting vector and the energy density respectively.
		\ This method may provide some insight into what information the \ stress-energy-momentum tensor contains."], "Text"], Cell[TextData[ "Any equation written with 4-vectors can be rewritten with quaternions.
		The rest of that tensor is \ generated by the second line.
	world.std.com /~sweetser/quaternions/notebooks/4tensor.nb (718 words)

	Re: Stress Energy tensor
		These values fill out the first column of the stress energy tensor.
		In Reply to: Re: Stress Energy tensor posted by dlgoff on September 30, 2002 at 18:34:24:
		This is the average change in energy, across the square
	superstringtheory.com /forum/partboard/messages14/187.html (358 words)

	Citebase - Towards possibility of self-maintained vacuum traversible wormhole
		The massless conformally coupled scalar field is characterized by the so-called "new improved stress-energy tensor", which is capable of classically violating the null energy condition.
		The renormalised vacuum expectation values of massless fermion (conventionally call it neutrino) stress-energy tensor are calculated in the static spherically-symmetrical wormhole topology.
		We find that for metric tensor sufficiently slow varied with distance violation of the averaged weak energy condition takes place irrespectively of the detailed form of metric.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/9612013 (942 words)

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