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	Articles - Static spacetime (Site not responding. Last check: 2007-10-05)
		In general relativity, a spacetime is said to be static if it admits a global, nowhere zero, timelike hypersurface orthogonal Killing vector field.
		In a static spacetime, the metric components may be chosen so that they are all independent of the time coordinate.
		It is in this sense that a static spacetime derives its name, as the geometry of the spacetime does not change.
	www.mainearth.com /articles/Static_spacetime (88 words)

	[No title]
		A spacetime exhibiting such features was recently discovered as a solution to a scale-invariant higher- derivative theory of gravity [22 ], and was later found to be a solution to c = 1 Liouville gravity [23 ] as well as to a non-critical string theory in two spacetime dimensions [24, 25 ].
		We mention that if an 2 analog to Hawking's area theorem [30 ] holds in two spacetime dimensions, it must actually state that the size of a fl hole never increases, which is exactly the opposite of what happens in four dimensions, and we note the difficulty in interpreting the "size" of a fl hole.
		By a spacetime (M, gab) we shall mean a Hausdorff C1 manifold M (with- out boundary) of dimension 2 with a non-degenerate Lorentzian metric gab, that is, a metric of signature (-, +,.
	jdc.math.uwo.ca /papers/causal.txt (2482 words)

	Space Age: Faster than light?
		This is because the geometry of Minkowski spacetime is complex, i.e.
		Furthermore, this dynamic relative speed is represented on the space/time diagram as an imaginary angle; the corresponding static speed is then the tangent of this angle.
		The speed of light on the Minkowski space/time diagram is infinite, because it uses dynamic speed, not static speed.
	www.astronist.demon.co.uk /space-age/sa82.html (971 words)

	Read about Physics at WorldVillage Encyclopedia. Research Physics and learn about Physics here! (Site not responding. Last check: 2007-10-05)
		This describes how the stress-energy tensor creates curvature of spacetime and forms the basis of general relativity.
		Einstein believed in a static universe and tried (and failed) to fix his equation to allow for this.
		However, by 1929 Edwin Hubble argued that astronomical observations demonstrate that the universe is expanding.
	encyclopedia.worldvillage.com /s/b/Physics (2153 words)

	4.3 Lensing in spherically symmetric and static spacetimes
		imply that the lightlike geodesics in a spherically symmetric static spacetime are equivalent to the light rays in a medium with index of refraction (74
		It reduces the lightlike geodesic problem in a spherically symmetric static spacetime to a standard problem in ordinary optics, as treated, e.g., in [212], §27, and [199], Section 4.
		The radial caustic is a lightlike surface in spacetime unless at points where it meets the axis; its projection to space is rotationally symmetric around the axis.
	univie.ac.at /EMIS/journals/LRG/Articles/lrr-2004-9/articlesu16.html (2004 words)

	Time [Internet Encyclopedia of Philosophy]
		Spacetime is four-dimensional and a continuum, with time being a distinguished, one-dimensional sub-space of this continuum.
		Proper time along a worldline in 4-d spacetime is the time elapsed by an object having that worldline, as shown on an ideal clock having the same worldline.
		The absolute theories imply that spacetime could exist even if there were no physical objects and events in the universe, but relational theories imply that spacetime is nothing but objects, their events, and the spatiotemporal relationships among them.
	www.iep.utm.edu /t/time.htm (15578 words)

	The Tom Bearden Website
		Spacetime curvature engines produce forces on mass components, telling them how to move and structure and forcibly changing their dynamics and structure.
		Matter in the target zone can be time-charged with a deterministic spacetime curvature engine, and the engine applied to the matter through a process of excitation decay as described in the foregoing paragraph, to cause desired changes in the matter.
		The forces and patterns (also called spacetime curvature engines) arise from every point within masses present in the zone during the period of time-charge excitation decay within the zone, and do not propagate in the manner of conventional force fields through the space intervening between the transmitters and the interference zone.
	www.cheniere.org /patent%20application/claim.htm (16713 words)

	Spacetime Stereo: Shape Recovery for Dynamic Scenes (Site not responding. Last check: 2007-10-05)
		This paper extends the traditional binocular stereo problem into the spacetime domain, in which a pair of video streams is matched simultaneously instead of matching pairs of images frame by frame.
		First, spacetime stereo serves as a general framework for structured light scanning and generates high quality depth maps for static scenes.
		Second, spacetime stereo is effective for a class of natural scenes, such as waving trees and flowing water, which have repetitive textures and chaotic behaviors and are challenging for existing stereo algorithms.
	csdl.computer.org /comp/proceedings/cvpr/2003/1900/02/190020367abs.htm (261 words)

	The New Redshift Interpretation Affirmed (Site not responding. Last check: 2007-10-05)
		Despite its long acceptance, this corollary was recently shown to be incorrect when I reported the discovery [1] of A New Redshift Interpretation (NRI) of the Hubble relation and the 2.7K CBR based on the premise that the universe is governed by Einstein's static-spacetime general relativity, rather than Friedmann-Lemaitre expanding-spacetime general relativity.
		Thus when C&S characterize the NRI as a static cosmological model in Sections 1, 3, 4 and 5, and use this erroneous assumption to claim the NRI fails several different tests, they are in reality waging a war against a straw-man argument of their own devising.
		Completely aside from their misidentifying the NRI as a static cosmological model, it is ironic that they raise the issue of consistency with general relativity because in gr-qc/9086061 I have already reported on two matters of considerable importance considering this point.
	www.halos.com /reports/arxiv-1998-affirmed.htm (2066 words)

	Gemtry (Site not responding. Last check: 2007-10-05)
		First, it was thought that uniform spacetime expansion showed promise for eliminating the implication of the Galaxy occupying a preferred position in the universe.
		That is, since spacetime expansion is assumed to be uniform, co-moving galactic separation must likewise be uniform, which implies that all observers, regardless of location, should see the same general picture of the universe.
		In it the Hubble redshifts are now interpreted solely in terms of relativistic Doppler and Einstein gravitational redshifts, all cast within the framework of a finite, non-homogeneous, vacuum-gravity universe with Universal center (C) near the Galaxy.
	evolution-facts.org /Gentry.htm (2715 words)

	A scalar invariant and the local geometry of a class of static spacetimes
		The scalar invariant, Iequivalent toR(munurhosigma;delta) R-munurhosigma;delta, constructed from the covariant derivative of the curvature tensor is used to probe the local geometry of static spacetimes which are also Einstein spaces.
		Futhermore, if ((3))Sigma is conformally flat it follows that every non-trivial static solution of the vacuum Einstein equation with a cosmological constant, is either Nariai-type or Kottler-type the classes of spacetimes relevant to quantum aspects of gravity.
		Manash Mukherjee, F P. Esposito, and LCR Wijewardhana, "A scalar invariant and the local geometry of a class of static spacetimes" (2003).
	repositories.cdlib.org /postprints/254 (151 words)

	static spacetimes - Information Technology Services (Site not responding. Last check: 2007-10-05)
		These are properties of congruences in a spacetime, not the spacetime itself.
		A static spacetime is usually defined by imposing an extra condition on a stationary spacetime (eg Wald p.
		I wasn't aware that this was a definition of a static spacetime.
	www.physicsforums.com /archive/forum/t-51949_static_spacetimes.html (861 words)

	A New Redshift Interpretation (Site not responding. Last check: 2007-10-05)
		A nonhomogeneous universe with vacuum energy, but without spacetime expansion, is utilized together with gravitational and Doppler redshifts as the basis for proposing a new interpretation of the Hubble relation and the 2.7K Cosmic Blackbody Radiation.
		First, uniform spacetime expansion showed promise for eliminating the implication of the Galaxy occupying a preferred position in the universe.
		That is, since spacetime expansion is assumed to be uniform, comoving galactic separation must likewise be uniform, which implies that all observers, regardless of location, should see the same general picture of the universe.
	www.halos.com /reports/arxiv-1998-redshift.htm (2278 words)

	5.1 Schwarzschild spacetime
		The Schwarzschild metric is static on the region
		For the Schwarzschild spacetime, the escape cones were first mentioned in [249, 223], and explicitly calculated in [320].
		For a perfect fluid with constant density, this is not the case; the resulting spacetime is then asymptotically simple, i.e., all inextendible light rays come from infinity and go to infinity.
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2004-9/articlesu18.html (2796 words)

	The New Redshift Interpretation Affirmed - Robert Gentry (Site not responding. Last check: 2007-10-05)
		Their analysis assumes the NRI represents a static cosmological model of the universe.
		Next, in claiming the standard cosmology is error free, CandS fail to respond to the contradictory evidence in my preprint, see report.
		There I first show why the universe is governed by Einstein static-spacetime GR, and not the Friedmann-Lemaitre expanding spacetime paradigm on which Big Bang cosmology is critically hinged.
	www.creationists.org /robertgentry/abstract1.html (227 words)

	[No title] (Site not responding. Last check: 2007-10-05)
		Persistence is a dynamic process (i.e., a dynamic activity); spacetime, however, is a static, geometric structure.
		Although spacetime is static, the mind perceives this 4-dimensional structure as unfolding.
		Duration (i.e., temporal passage) is not a dimension of spacetime.
	home.att.net /~Andemicael/Paper_Clarif.html (636 words)

	[No title] (Site not responding. Last check: 2007-10-05)
		Indeed, Weyl's solutions are precisely the static axisymmetric vacuum solutions in gtr, and they have a simple and beautiful relationship to the corresponding Newtonian solutions: each Weyl solution arises from a Newtonian static axisymmetric vacuum potential, and in the weak field limit, the Newtonian potential is recovered from the Weyl solution.
		These are static axisymmetric solutions to the EFE, with nonzero stress energy tensor in the disks, and which asymmetric pressures and stresses in the disks, in general, so that they should be regarded as elastic solids.
		It makes sense to talk about the metric of a spacetime, but not to refer to coordinate dependent properties of the appearance of the components of the metric tensor in a particular coordinate basis, such as the property of having off diagonal terms (which is what I guess you mean by "mixed terms").
	www.math.ucr.edu /home/baez/PUB/weylvac (4548 words)

	Being and Becoming in Modern Physics
		For our purposes, the key change from Newtonian spacetime to Minkowski spacetime is that in the latter it is no longer the case that the temporal interval between any two points or events in the spacetime, p and q, is a well-defined quantity.
		In fact, the temporal interval between two points in the spacetime (and hence the simultaneity of two points in the spacetime) is not defined at all until a coordinate system or frame of reference (with some arbitrarily chosen spacetime point as origin of the frame) is chosen.
		Wilfrid Sellars believed that the various invariant or observer-independent elements of Minkowski spacetime (like the light cone structure to be described below) that are typically given primary consideration in treatments of relativity from a spacetime perspective are abstractions from and secondary to the ‘perspectival’ pictures, the myriad of coordinate systems or reference frames.
	plato.stanford.edu /entries/spacetime-bebecome (8948 words)

	Strange Meeting
		We find that the spacetime manifold at this boundary need not be considered as singular, because it can be shown that the singularity is removable, in the sense that all the invariant measures of the field smoothly approach fixed finite values as r approaches 2m from either direction.
		Hence it could be argued that the field equations were superfluous to the determination of the spherically symmetrical static spacetime metric.
		Naturally if such direct conveyance between widely separate regions of spacetime were possible, and if those regions were also connected by (much longer) ordinary timelike paths, this raises the prospect of various kinds of "time travel", assuming a wormhole connected to the past was somehow established and maintained.
	www.mathpages.com /rr/s8-07/8-07.htm (3124 words)

	Outline of the course Geometry of SpaceTime
		The equivalence principle in its weak form and Einstein's lift Gedanken experiment; (local)equivalence between uniform gravitational fields and inertial fields; gaussian coordinate systems, description of physical properties by means of geometrical properties of the spacetime continuum; relation between the principle of general covariance, Einstein's equivalence principle and theory of the gravitational field.
		Heuristic derivation of Einstein equations in a static spacetime by the analysis of the weak field limit.
		mathematical formulation of spacetime as a Lorentzian manifold; physical interpretation of geometrical entities associated with the concept of manifold: exponential map, geodesics, normal coordinate systems and their relations with the physical concepts of free motion, causal structure and equivalence principle.
	www-dft.ts.infn.it /~ansoldi/Didactics/Teaching/SpaceTimeCourse/Web/ProgEng.html (1059 words)

	[No title] (Site not responding. Last check: 2007-10-05)
		It also furnishes a very nice illustration of dynamic versus static coordinate patches (again providing a very nice foil to the analogous patches in the Kruskal vacuum), and of the use of Kruskal-like coordinates and a Penrose diagram to understand the (surprising!) global geometry and causal structure.
		Now we seek a static -planar- symmetric metric, of the form ds^2 = -f(x)^2 dt^2 + h(x)^2 dx^2 + g(x)^2 (dy^2 + dz^2) ^^^^^^^^^^^^^^^^^^^ where the metric of a plane x = x0 is underlined (substitute x = x0).
		IOW, for a static observer looking toward the near plate, a -small- object in his line of sight appears undistorted, but closer than it really is. The magnification factor is greater closer to the plates.
	math.ucr.edu /home/baez/PUB/thread (4201 words)

	[No title] (Site not responding. Last check: 2007-10-05)
		In a static spacetime, the Killing time can be used to measure the time required for signals or objects to propagate between two of its orbits.
		We prove a simple theorem to the effect that in any spacetime satisfying the weak energy condition the above signaling time is, in this sense, no faster than that for a corresponding signal in Minkowski space.
		Our examples suggest that signaling in spacetimes satisfying this stronger energy condition may be significantly slower than the fastest spacetimes satisfying only the weak energy condition.
	www.physics.umd.edu /grt/ecgm/abstracts/cabrera.html (157 words)

	[No title]
		If spacetime is a unified state of affairs then any change of state in space requires that the space itself change, by definition, since space is defined mathematically and physically by its states and by nothing else.
		We disagree on a very important and fundamental point: I claim that spacetime is static, and you hold that it is not.
		I believe, however, that it is the mind's persisting mental states perceiving/observing successive points of a static spacetime which give the impression of an unfolding universe.
	home.att.net /~Andemicael/jcs2.html (1042 words)

	SPACETIME! (Site not responding. Last check: 2007-10-05)
		Spacetime is, not surprisingly, the union of space and time.
		Figure 5 is a representation of the Flatlandian life (crunched down into several inches): A square is born, a line is born; they meet, have a baby square, and die.
		It is very uncertain as to whether future spacetime is as static as past spacetime--if the past is static at all!
	www.brown.edu /Students/OHJC/ma8/papers/st_intro.htm (539 words)

	Mach Principle and Energy-Momentum Conservation in Einstein General Relativity
		The question that arises is to what extent the nonrotating coordinates may continue to be assumed static for the study of the dynamics of test bodies in a static gravitational field.
		A special class of coordinates, the nonrotating coordinates, is established by means of a variational principle imposed on the spacetime integrals of the components of the energy-momentum tensor.
		5) In static spacetime, and with an appropriate tensorial definition of gravitational energy-momentum, they are adaptable to the static nature of spacetime.
	www.liberal.org.il /physics/mach.htm (2774 words)

	[No title] (Site not responding. Last check: 2007-10-05)
		For instance, if a spacetime is static, d/dt is a Killing vector, and the corresponding conserved quantity is energy.
		If a spacetime has central S^2 symmetry, then if we right the metric of the sphere ds^2 = du^2 + sin^2 u dv^2 then there are three Killing fields, and the corresponding conserved quantities are the angular momenta.
		The acceleration required to maintain static position is q q [ 2 m ] a = ---------------- e_r ~ ----------- [ 1 + ------ ] e_r r (m - log(r))^2 r (log(r)^2 [ log(r) ] These all vanish as r -> infinity.
	math.ucr.edu /home/baez/PUB/einsteinmaxwell (2953 words)

	String Mechanics
		Rather, the universe is expanding, thus it is not static, and furthermore unavoidable quantum fluctuations of the metric tensor guv (x) defy the fixed and smooth description of the spacetime manifold, at least at very short distances.
		One, of course, tacitly assumes the existence of a fixed, smooth spacetime background that does not "disturb" the system, acting simply as the arena in which things are happening, and thus leaving the system "closed".
		In principle, in fixed, smooth spacetime backgrounds, hopefully corresponding to critical points in our new stringy language, there is a decoupling of the global states from the local, low-energy states in (22), i.e., all cg's do vanish, and thus implying vanishing beta j in (23).
	www.qedcorp.com /pcr/pcr/nanopou5.html (5242 words)

	General relativistic forces in non-static spacetimes (Site not responding. Last check: 2007-10-05)
		Essentially, it explains the bending of a path in a gravitational field as being due to the curvature of spacetime, instead of to a force.
		An early attempt to avoid this restriction extended to conformally static spacetimes [12].
		To demonstrate the reality of gravitational waves, Ehlers and Kundt [14] considered a sphere of test particles in the path of a plane wave and demonstrated that momentum was imparted to the particles and the sphere was distorted.
	www.sif.it /cimento/tocb/112.02-03/31/31.html (1784 words)

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