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	Rindler coordinates - Wikipedia, the free encyclopedia
		In relativistic physics, the Rindler coordinate chart is an important and useful coordinate chart representing part of flat spacetime, also called the Minkowski vacuum.
		Thus, the spatial coordinates in the Rindler chart have a very simple interpretation consistent with the claim that the Rindler observers are mutually stationary.
		Born coordinates, for another important coordinate system adapted to the motion of certain accelerated observers in Minkowski spacetime.
	en.wikipedia.org /wiki/Rindler_coordinates (2597 words)

	UFO Area Black Holes and Event Horizons (Site not responding. Last check: 2007-09-08)
		In fact, he credits Rindler with having coined the term "event horizon" [and "particle horizon"] in a 1956 paper.
		In Schwarzschild coordinates it is defined by R Total Mass-Energy Inside Radius R = INTEGRAL 4pi r^2 rho dr r=0 The fully convincing argument for this definition is found only by considering a generalization of it to time-dependent spherically symmetric stars (pulsating, collapsing, or exploding).
		For them one finds that the mass-energy M associated with a given ball of matter (fixed bayron number) can change in time only to the extent that locally measurable energy fluxes can be detected at the boundary of the ball.
	www.ufoarea.com /physics_cosmology_black_holes_event.html (2329 words)

	PY341 HW#12 (Site not responding. Last check: 2007-09-08)
		The coordinates v and rho are defined by t = gamma * v * rho and x = gamma * rho.
		Show that the redshift factor between an inertial observer and a Rindler (constant acceleration) observer L is given by K = exp(tau/rho), where tau = proper time along L's worldline and rho = proper distance between L and the origin.
		Use this along with the relation x^2 - t^2 = rho^2 to obtain t_2 and x_2 (the coordinates of the event at which the Rindler observer detects the first signal from the inertial observer).
	wonka.physics.ncsu.edu /~jbrown/PY341_Sp01/HOMEWORK/hw12.html (362 words)

	Packing Universes In Spacetime
		He postulated a cloud of particles expanding in flat spacetime from a single event O, with a distribution of velocities such that the mutual velocities between neighboring particles was the same for every particle, just as in the one-dimensional case described at the beginning of this section.
		To determine the density with respect to the inertial coordinates t,x,y,z, we first consider the density in the radial direction at a point on the x axis at time t.
		This distribution applies to every inertial system or coordinates with origin at O, so this cosmology looks the same, and is spherically symmetrical, with respect to the rest frame of each individual particle.
	www.mathpages.com /rr/s7-05/7-05.htm (1491 words)

	TSRI - News & Views
		Duties: Staffing the Beckman Building front desk during the evening shift, 3:45 PM to 12:15 AM, which includes providing security for the building, acting as emergency operator and radio dispatcher, and monitoring numerous building systems, including freezers, ventilation, and alarms.
		Together the volunteers provide refreshments, blow up balloons, shake hands, take care of children, and make signs for family members to mark the occasion when a ship, submarine, aircraft carrier, or plane returns.
		Rindler is long-time chair of the Navy League's "Operation Welcome Home" Committee.
	www.scripps.edu /newsandviews/e_20041004/rindler.html (276 words)

	General Relativity. Note 2 (Site not responding. Last check: 2007-09-08)
		The non-inertial Rindler frame (named after Wolfgan Rindler?) is made of constantly, uniformly accelerated clocks.
		The Rindler frame is very useful as a model of a constant uniform gravitational field.
		We shall see on the example of the Rindler frame that non-inertial frames have some peculiar features: they are curved, they have horizons, time goes differently at different places.
	www.phys.au.dk /subatom/nucltheo/GTR/note2.htm (501 words)

	Re: gravity from spacetime thermodynamics
		That is, we do not need to consider arbitrary static spacetimes in arbitrary coordinates only to then make a change of coordinates to a local Rindler system.
		We can pick a flat spacetime in Rindler coordinates from the outset and require that the boundary term of the action (4) has the desired value.
		One is so used to switching to convenient coordinates when necessary.) I'll summarize the outline of the proof as I now imagine it, after thinking about your comments: Start with a family of theories of a field g_ab, each given by an element A' of the family of actions eq.
	www.lns.cornell.edu /spr/2002-11/msg0045592.html (690 words)

	2nd Vienna Central European Seminar on Particle Physics and Quantum Field Theory, 2005 (Site not responding. Last check: 2007-09-08)
		The entropy S of the horizon θ = π/2 of the Hawking wormhole written in spherical Rindler coordinates is computed in this paper.
		Using Padmanabhan's prescription, we found that the surface gravity of the horizon is constant and equals the proper acceleration of the Rindler observer.
		S is a monotonic function of the radial coordinate ξ and vanishes when ξ equals the Planck's length.
	www.univie.ac.at /vienna.seminar/2005/abstracts/abstr_Culetu.html (77 words)

	Resonant Modes of a Conical Cavity
		This allows the problem to be treated exactly in spherical polar coordinates, with all three boundaries being surfaces with constant values for one or other of the coordinates.
		We are interested in the distribution of force on the walls, and it is obvious from the axial symmetry (of both the cavity itself and the fields we're considering) that if we integrate over a cross-section of the wall taken in a plane orthogonal to the z-axis — i.e.
		coordinate — the net force on each such cross-section will be directed solely along the z-axis.
	gregegan.customer.netspace.net.au /SCIENCE/Cavity/Cavity.html (4454 words)

	Rindler coordinates (Site not responding. Last check: 2007-09-08)
		The Rindler coordinate system describes a uniformly accelerating frame of reference in Minkowski space.
		It is possible to use another coordinate system with the coordinates
		This coordinate system does not cover the whole of Minkowski spacetime but rather a wedge (called a Rindler wedge or Rindler space).
	read-and-go.hopto.org /Relativity/Rindler-coordinates.html (178 words)

	Physics 675, Fall 2005
		a local inertial coordinate system at a point the Christoffel symbols vanish, so the covariant acceleration is simply equal to the second derivative of the curve coordinates with respect to the path parameter.
		I derived this in a simpler way than did Hartle: translational symmetry implies that the coordinate wavelength is conserved as a wave propagates, therefore the proper wavelength scales with the scale factor.
		Since the integral of the coordinate increment dx is the same for both rays, one infers a relation between the emission and reception time intervals, which reproduces the wavelength redshift when a(t) is nearly constant over the emission interval.
	www.physics.umd.edu /grt/taj/675b/675bnotes.html (8554 words)

	Unruh effect - Wikipedia, the free encyclopedia
		The energy states of any quantized field are defined by the Hamiltonian, based on local conditions, including the time coordinate.
		This decomposition happens to be different in Cartesian and Rindler coordinates (although the two are related by a Bogoliubov transformation).
		Just as the Rindler spacetime can be seen as a toy model for fl holes and cosmological horizons, the Unruh effect provides a toy model to explain Hawking radiation.
	en.wikipedia.org /wiki/Unruh_effect (673 words)

	The Gravitational Field of a Directed Beam of Light
		The linearized Einstein field equations are [Rindler pg.
		Therefore a test light ray moving in the +x direction, the same direction as the flow of radiation has the same speed regardless of where in the field the ray is located.
		If the ray is moving in the opposite direction the speed of light depends on the spatial coordinates as is usual for motion if a gravitational field.
	www.geocities.com /physics_world/gr/grav_light.htm (478 words)

	[No title] (Site not responding. Last check: 2007-09-08)
		The difference is essentially that different timelike curves in spacetime (world lines) passing through a pair of distinct events will have in general different "total squared intervals" (squared "length").
		The case B = 0 reduces to our null geodesics whose trajectories agree with our unique ray emerging from the Rindler horizon x = 0.) Thus, we have now outlined three independent methods of obtaining the null geodesics in the Rindler chart.
		I hope the discussion of the Rindler chart above will help you understand the physical experience of one family of accelerating observers.
	math.ucr.edu /home/baez/PUB/rindlerchart (636 words)

	Quantum tunneling not faster than light - Bad Astronomy and Universe Today Forum
		I highly recommend that you read a bit about the Rindler horizon (and Rindler coordinates.) This is that case that I mentioned earlier with an observer experiencing constant acceleration, and this also shows the presence of a horizon even though you can transform everything back to a global Lorentz frame (i.e.
		Schwarzschild coordinates) around a static spherical mass is a non-inertial coordinate system.
		This is not the case in classical Newtonian gravity where the equivalent of Schwarzschild coordinates do form an inertial coordinate system.
	www.bautforum.com /showthread.php?p=797361 (3643 words)

	Topics: Rindler Space (Site not responding. Last check: 2007-09-08)
		Idea: Minkowski st with coordinates adapted to a boost kvf, i.e., to a uniformly accelerated observer.
		Coordinates: If (X, T) are the Minkowski coordinates, Rindler coordinates (x, t) are defined on the right wedge (X > 0,
		Idea: The Minkowski vacuum looks like a thermal state in Rindler space, for an observer moving along x = const, with temperature depending on its acceleration.
	www.phy.olemiss.edu /~luca/Topics/st/rindler.html (180 words)

	Four-vector (Site not responding. Last check: 2007-09-08)
		In relativity, a four-vector is a vector in a four-dimensional real vector space, called Minkowski space, whose components transform like the space and time coordinates (''t'', x, y, z) under spatial rotations and boosts (a change by a constant velocity to another inertial reference frame).
		The set of all such rotations and boosts, called Lorentz transformations and described by 4×4 matrices, forms the Lorentz group.
		Rindler, W. Introduction to Special Relativity (2nd edn.) (1991) Clarendon Press Oxford Order: ISBN 0-19-853952-5
	four-vector.iqnaut.net (782 words)

	► » Horizons (Site not responding. Last check: 2007-09-08)
		In the accelerated coordinates the Rindler horizon remains at x'=-1/a;
		Rindler horizon -- it is SIMILAR but not really correct).
		this light remains behind the Rindler horizon and is never observable.
	www.physics-talk.com /Horizons-6016172.html (2124 words)

	Citebase - Static, massive fields and vacuum polarization potential in Rindler space
		Authors: Linet, B. In Rindler space, we determine in terms of special functions the expression of the static, massive scalar or vector field generated by a point source.
		We find also an explicit integral expression of the induced electrostatic potential resulting from the vacuum polarization due to an electric charge at rest in the Rindler coordinates.
		For a weak acceleration, we give then an approximate expression in the Fermi coordinates associated with the uniformly accelerated observer.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/9704007 (151 words)

	Amazon.com: "flat coordinates": Key Phrase page (Site not responding. Last check: 2007-09-08)
		g and a tensor field A of rank 3 such that if we write the components of.4 in local g-flat coordinates, the conditions of 0.4.1 a) and eventually b) are satisfied.
		So local flat coordinates t1,...,tn on M exist such that the metric in these coordinates is constant at at avP av9gP9(v) = 1j =...
		These two additional coordinates are not relevant for our considerations.
	www.amazon.com /phrase/flat-coordinates (557 words)

	Re: EP and Unruh - effect (Layman)
		His theory isn't vulnerable to the counterargument, because in the M -> infinity limit you end up with privileged Rindler coordinates and the associated Rindler energy, in terms of which we all agree (I think?) that the particle doesn't radiate.
		I would be particularly interested to know whether the result depends on whether you use the advanced or retarded potential.
		Actually, it's obvious that it does differ if you include the regions not covered by Rindler coordinates, which is quite interesting.
	www.lns.cornell.edu /spr/2005-07/msg0070413.html (611 words)

	Luboš Motl: The Reference Frame: May 2005 (Site not responding. Last check: 2007-09-08)
		First of all, one of the homogeneous coordinates in CP3 had to be set to zero which means that we really display the intersection of a K3 surface with a hyperplane.
		The other three coordinates parameterizing a CP2 were reinterpreted as a C2 and another projection from 4 real dimensions to 3 real dimensions was applied in different ways parameterized by "time".
		One obtains a non-flat eleven-dimensional geometry in which ten coordinates shrink as we approach the Big Bang while the eleventh coordinate expands.
	motls.blogspot.com /2005_05_01_motls_archive.html (12187 words)

	A Mechanism for Accelerated Radioactive Decay
		While Kaluza required that physical quantities of ordinary spacetime should have zero or vanishingly small derivatives with respect to the fifth coordinate, Klein wanted to replace this assumption by the requirement that physical quantities be periodic with respect to this coordinate.
		The four dimensional version of this equation is know in quantum physics as the Klein-Gordon equation (Kragh, 1984), and is applied to particles of spin zero.
		Choosing the coordinate of the compactified fifth dimension so that it varies from 0 to 2p, then the wavefunction j has the period 2p in the fifth-dimension coordinate x
	www.creationresearch.org /crsq/articles/37/37_1/chaffin/acceldecay.html (3642 words)

	Citebase - Quantum charged fields in Rindler space
		We study, using Rindler coordinates, the quantization of a charged scalar field interacting with a constant, external, electric field.
		First we establish the expression of the Schwinger vacuum decay rate, using the operator formalism.
		Our analysis reinforces the conjecture which identifies the zero winding sector of the Minkowski propagator with the Rindler propagator.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/9912016 (240 words)

	Physics: Faculty and Research: Wolfgang Rindler
		Professor Rindler focuses his research on theoretical relativistic cosmology and on basic problems in general relativity.
		He also authored or co-authored seven books, several of which have been translated into foreign languages (Russian, Japanese, etc.)
		Rotating coordinates as tools for calculating circular geodesics and gyroscopic precession.
	www.utdallas.edu /physics/faculty/wolfgang.html (157 words)

	UTD Physics: Astrophysics, Cosmology, and Relativity
		Extended studies of current and future constraints on dark energy parameters from cosmic complementarity (CMB+weak gravitational lensing+supernova data) and cosmic shear tomography.
		Studies using perfect fluid models in non-comoving null spherical (observational) coordinates
		James is exploring an inverse approach to Einstein’s equations in the presence of various dark energy backgrounds and the use of null (observational) coordinates in this framework
	www.utdallas.edu /~mishak/relativitycosmology.html (579 words)

	Black Hole Entroy
		equivalence) and 2) that the entropy of a horizon (in a Rindler frame)
		Rindler horizons in static spacetimes have the desired entropy/area
		spacetime in Rindler coordinates from the outset and require that the
	www-stud.uni-essen.de /~sb0264/BHEntropy.html (3909 words)

	Thanks to Jacques \| The String Coffee Table
		In any case, the Goheer et al paper was was about the entropy of Rindler space.
		BTW, the connection from your theory to Rindler space is by considering an accelerated observer, right?
		And yes, the Rindler coordinates just arise because the observer is accelerating.
	golem.ph.utexas.edu /string/archives/000265.html (2788 words)

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