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	Einstein's Field Equations
		We will see later that this equation gives rise to a continuity equation and the equation of motion when we take the energy-momentum tensor to be some general type of fluid filling up the spacetime manifold.
		Einstein considered this equation but rejected it since it does not reduce down to the Newtonian gravitational equations in the form of the Poisson's equation, the necessary 2nd order form when matter is present in Newton's theory.
		The field equations (14.9) reduce properly to the Newtonian Poisson equation.
	io.uwinnipeg.ca /~vincent/4500.6-001/Cosmology/Field-Equations.htm (648 words)

	Maxwell’s Electromagnetic Field Equation No. 1 (Site not responding. Last check: )
		The differential form of the equation states that the divergence or outward flow of electric flux from a point is equal to the volume charge density at that point.
		This equation states that the effective electric field through a surface enclosing a volume is equal to the total charge within the volume.
		The equation states that the divergence of the electric flux density at a point is equal to the charge per unit volume at that point.
	www.iit.edu /~smile/guests/gsmxsec1.htm (3180 words)

	NationMaster - Encyclopedia: Einstein's field equation (Site not responding. Last check: )
		In physics, the Einstein field equation or Einstein equation is a differential equation in Einstein's theory of general relativity.
		Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, which exerts a force on those particles that possess a property known as electric charge, and is in turn affected by the presence and motion of such particles.
		In general relativity, Einsteins field equations can be derived from an action principle starting from the Einstein-Hilbert action: where g is the (pseudo)Riemannian metric, R is the Ricci scalar, n is the number of spacetime dimensions and k is a constant which depends on the units chosen...
	www.nationmaster.com /encyclopedia/Einstein's_field_equation/Solutions_of_the_field_equations (2833 words)

	Electric Field Intensity
		Electric field strength is location dependent, and its magnitude decreases as the distance from a location to the source increases.
		Yet the field strength is defined as the effect (or force) per sensitivity of the detector; so the field strength of a stinky diaper or of an electric charge is not dependent upon the sensitivity of the detector.
		The stinky field analogy proves useful in conveying both the concept of an electric field and the mathematics of an electric field.
	www.glenbrook.k12.il.us /GBSSCI/PHYS/CLASS/estatics/u8l4b.html (2098 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: )
		The Einstein field equations (EFE) are a set of ten equations in Einstein's theory of general relativity in which the fundamental force of gravitation is described as a curved spacetime caused by matter and energy.
		The EFE collectively form a tensor equation and equate the curvature of spacetime (as expressed using the Einstein tensor) with the energy and momentum within the spacetime (as expressed using the stress-energy tensor).
		One way of solving the field equations is to make an approximation, namely, that far from the source(s) of gravitating matter, the gravitational field is very weak and the spacetime approximates that of Minkowski space.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Einstein_field_equations (1276 words)

	Science Fair Projects - Einstein's field equation
		In physics, the Einstein field equation or Einstein equation is a tensor equation in the theory of gravitation.
		The Einstein field equation describes how space-time is curved by matter, and (the other way round) how matter is influenced by the curvature of space-time (i.e.
		Einstein's equation reduces to Newton's law of gravity by using both the weak-field approximation and the slow-motion approximation.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Einstein_field_equation (661 words)

	Einstein's field equation - Biocrawler (Site not responding. Last check: )
		In physics, the Einstein field equation or Einstein equation is a equation in Einstein's theory of general relativity.
		An important consequence of the EFE is the local conservation of energy and momentum; this result arises by using the differential Bianchi identity to obtain
		Mathematicians usually refer to manifolds with a vanishing Ricci tensor as Ricci-flat manifolds and manifolds with a Ricci tensor is proportional to the metric as Einstein manifolds.
	www.biocrawler.com /encyclopedia/Einstein%27s_field_equation (1078 words)

	Abstract
		Where λ is the charge density of the electric field, and r is the radial distance from the center of the cylinders, measured in meters.
		Solving the equation is possible as the voltage at point a (Va) and the inner and outer radii of the cylinders are known quantities.
		Equation 6 can be formatted to any two points in the field, and not just the inner and outer radii.
	people.msoe.edu /~lannanm/lab_ph230_5.html (863 words)

	Einstein's field equation
		In physics, the Einstein field equation or the Einstein equation is an equation in the theory of gravitation, called general relativity, that describes how matter creates gravity and, conversely, how gravity affects matter.
		The Einstein field equation reduces to Newton's law of gravity in the non-relativistic limit (that is: at low velocities and weak gravitational fields).
		These equations are the core of the mathematical formulation of general relativity.
	www.casimiro.com /wiki/en/wikipedia/e/ei/einstein_s_field_equation.html (613 words)

	math lessons - Field equation
		A field equation is an equation in a physical theory that describes how a fundamental force (or a combination of such forces) interacts with matter.
		The field equations of gravitation are Einstein's field equations which describe gravity as a 'curvature' of spacetime produced by the existence of matter.
		Modern field equations tend to be tensor equations.
	www.mathdaily.com /lessons/Field_equation (222 words)

	Einstein field equation (Site not responding. Last check: )
		In physics, the Einstein field equation or the Einsteinequation is an equation in the theory of gravitation, called general relativity, that describes how matter creates gravity and, conversely, how gravity affectsmatter.
		The Einstein field equation reduces to Newton's law of gravity in thenon-relativistic limit (that is: at low velocities and weak gravitational fields).
		A solution of the Einstein field equation is a certain metric appropriate for the given mass and pressuredistribution of the matter.
	www.therfcc.org /einstein-field-equation-15627.html (534 words)

	Reference.com/Encyclopedia/Einstein field equations
		The Einstein field equations (EFE) or Einstein's equations are a set of ten equations in Einstein's theory of general relativity in which the fundamental force of gravitation is described as a curved spacetime caused by matter and energy.
		The EFE collectively form a tensor equation and equate the curvature of spacetime (as expressed using the Einstein tensor) with the energy and momentum within the spacetime (as expressed using the stress-energy tensor).
		The equations in contexts outside of general relativity are still referred to as the Einstein field equations (if the dimension is clear).
	www.reference.com /browse/wiki/Einstein%27s_field_equations (1449 words)

	Magnetism: quantities, units and relationships
		Equation TMD suggests that the 'B field' is simply an effect of which the 'H field' is the cause.
		If the B field pattern around a bar magnet is compared with the H field then the lines of B form continuous loops without beginning or end whereas the lines of H may either originate or terminate at the poles of the magnet.
		You could argue that B indicates better the strength of a magnetic field than does the 'magnetic field strength' H! This is one reason why modern authors tend not to use these names and stick instead with 'B field' and 'H field'.
	www.ee.surrey.ac.uk /Workshop/advice/coils/terms.html (3382 words)

	The Field Equation and More (Site not responding. Last check: )
		As was mentioned in the first part of this article, Einstein's field equation is an equation that relates the presence of matter and energy to the curvature of space-time.
		On the right side of the field equation there is another tensor that represents the matter and energy that are present at a point.
		An exact solution of Einstein's equation is a formula for the metric at all the points (events) in time-space, which satisfies the field equation for a known physical case.
	www.polarhome.com:763 /~rafimoor/english/GRE3.htm (2245 words)

	1st-Order Approximation (Mean Field Theory)
		Equation (5) is exact in the case in which the states of different cells are completely uncorrelated.
		Substituting equation (5) into the equation of the form (2) for the evolution of the probability of a 1, we have the mean field equation
		That is, the mean field theory supplies a classification of cellular automata which is a strict refinement of the 0th-order classification.
	www.santafe.edu /~hag/class/node6.html (452 words)

	field_equation - The Wordbook Encyclopedia (Site not responding. Last check: )
		Before the theory of quantum mechanics was fully developed, there were two known field theories, namely gravitation and electromagnetism (these two are sometimes referred to as classical field theories, as they were formulated before the advent of quantum mechanics, and hence do not take into account quantum phenomena).
		The first field theory of gravity was Newton's theory of gravitation, which described gravity as obeying an inverse square law.
		The field equations of classical electromagnetism are Maxwell's equations which describe how electromagnetic fields are produced from charged particles and are written in the framework of special relativity (which was devised to consistently describe electromagnetism and classical mechanics) as:
	www.thewordbook.com /field_equation (676 words)

	INTRODUCTION
		This paper presents the derivation of equation (1), generalizes it, and suggests that it is universal fact.
		Equation (1) of Section 2 transforms to the energy equation, it is an isolated energy state.
		It is hoped that the reader is becoming aware of the thought process that there are electric fields, magnetic vector potentials and gravitational force fields implicit at the atomic level.
	home.comcast.net /~tjbesmer/Fields_Waves_and_Energy.htm (3647 words)

	Chapter 1
		The Yilmaz theory adds to the gravitational field equation of the Einstein theory a tensor to characterize the energy and stress of the gravitational field.
		The gravitational field equation of the Yilmaz theory is more complicated than that of the Einstein theory because it has an additional tensor that characterizes the energy and stress of the gravitational field.
		Equations derived from this model demonstrate that the universe should expand locally approximately in accordance with the Hubble Law.
	www.olduniverse.com /chapter_1.htm (1042 words)

	3,4. The Fundamental Field Equation and Characteristics
		Appreciating the energy field at the particle as well as in a region is central to the understanding of this theory.
		Solving the electromagnetic wave equation subject to the appropriate boundary conditions and assuming a waveguide of infinite length yields field expressions given in terms of Bessel functions of the first kind.
		In addition, just as the electromagnetic field can be circularly polarized (the macroscopic manifestation of the spin quantum number of the associated photons) leading to a spiraling of the field vectors in the circular waveguide, the density distribution of a particle in a diallel-quantum state may also be described as spiraling.
	www.allanstime.com /UnifiedFieldTheory/Original_Dec99/fundamental_field_equation.htm (2378 words)

	The Consequence of General Relativity
		When this model is put into the Einstein field equation, it turns out that the energy density or pressure has to take a negative value.
		Einstein considered this unacceptable and, in order to remedy the problem, he modified his field equation by inserting a new term, called "cosmological term", into it.
		Puting the Robertson-Walker metric into the Einstein field equation and assuming the perfect-fluid form for the energy-momentum tensor.
	hepth.hanyang.ac.kr /~kst/lect/relativity/x1535.htm (1074 words)

	3.1 Semiclassical gravity
		Semiclassical gravity describes the interaction of a classical gravitational field with quantum matter fields.
		The field may be quantized in the manifold using the standard canonical quantization formalism [25
		For a free quantum field this theory is robust in the sense that it is self-consistent and fairly well understood.
	relativity.livingreviews.org /Articles/lrr-2004-3/articlesu2.html (821 words)

	THE EINSTEIN EQUATIONS
		In a nutshell, this equation describes the properties of a gravitational field surroun ding a given mass.
		For a mathematician, the difficulties lie in the fact that the equations are nonlinear and coupled also and in their sheer number of terms.
		Physicists are motivated to grapple with the complexity of Einstein's field equations because they can be used, theoretically at least, to describe all possible spacetime scenarios, from the collisions of fl holes to the gravit ational interactions of irregular chunks of matter.
	archive.ncsa.uiuc.edu /Cyberia/NumRel/EinsteinEquations.html (1024 words)

	Einstein's field equation - Education - Information - Educational Resources - Encyclopedia - Music
		In physics, the Einstein field equation or the Einstein equation is an equation in the theory of gravitation, called general relativity, that describes how matter creates gravity and, conversely, how gravity affects matter.
		The Einstein field equation reduces to Newton's law of gravity in the non-relativistic limit (that is: at low velocities and weak gravitational fields).
		A solution of the Einstein field equation is a certain metric appropriate for the given mass and pressure distribution of the matter.
	www.music.us /education/E/Einstein%27s-field-equation.htm (776 words)

	Classical Unified Field Theory
		The equations of the first two papers are recast with the new definition of a quaternion derivative, resulting in a quantum unified field and force theory.
		The justification for investigating the unified field equation hypothesis is due to the presence of the Maxwell equations.
		From the perspective of this proposal, the freedom to choose a scalar gauge field for the Maxwell equations is due to the omission of the gravitational force field.
	www.theworld.com /~sweetser/quaternions/gravity/unified_field/unified_field.html (5812 words)

	Unified field equations
		For a connection that is metric compatible and torsion-free, second-order derivatives of the metric are part of the field equations.
		Although the field equations are rank one, the field strength tensor is second rank, consistent with arguments that a symmetric second-rank field strength tensor is required to characterize a dynamic metric.
		The homogeneous Maxwell equations are vector identities, unaffected by unification.
	world.std.com /~sweetser/quaternions/gravity/analog.v4.iop/node3.html (1047 words)

	DRAFT: Deducing a Unified Field Theory from Electromagnetism
		It is shown how the Rosen metric is a solution to the field equations, and thus is passes weak field tests of gravity to first-order Paraterized Post-Newtonian (PPN) accuracy, and is distinguisable from general relativity at second-order PPN accuracy.
		The complete wave equation is composed of the D'Alembertian operator acting on the potential, the divergence of the connection, the connection of the first derivative of the potential, and the connection of the connection.
		This field equation can account for all classical effects of Gauss' and Newton's law because it is identical to their superposition.
	theworld.com /~sweetser/quaternions/gravity/em2gem/em2gem.html (2641 words)

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