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	A note on the Lanczos potential
		Given the Weyl tensor, it may be a formidable task to construct a Lanczos generator by integrating directly the system (2) of differential equations for the unknown
		However, here we exhibit that the Lanczos potential, for the important geometry of Kerr [9], can be generated with remarkable simplicity.
		In fact, we consider the metric of a rotating fl hole [10] in Boyer-Lindquist [11] coordinates
	wbabin.net /bonilla/kerr.htm (257 words)

	Kerr metric - Wikipedia, the free encyclopedia
		In particular, the quadrupole moment of the Kerr vacuum vanishes; in this sense, it is the simplest rotating and stationary asympotically flat vacuum.
		The interior of the Kerr vacuum, or rather a portion of it, is locally isometric to the Chandrasekhar/Ferrari CPW vacuum, an example of a colliding plane wave model.
		This is particularly interesting, because the global structure of this CPW solution is quite different from that of the Kerr vacuum, and in principle, an experimenter could hope to study the geometry of (the outer portion of) the Kerr interior by arranging the collision of two suitable gravitational plane waves.
	en.wikipedia.org /wiki/Kerr_solution (835 words)

	Encyclopedia: Kerr metric (Site not responding. Last check: 2007-11-05)
		In general relativity, the Kerr metric describes the geometry of spacetime around a rotating massive body, such as a rotating fl hole.
		This famous exact solution was discovered in 1963 by the New Zealand born mathematician Roy P. Kerr.
		In mathematics, in Riemannian geometry, the metric tensor is a tensor of rank 2 that is used to measure distance and angle in a space.
	www.nationmaster.com /encyclopedia/Kerr-metric (1233 words)

	Expression Management (Site not responding. Last check: 2007-11-05)
		In this regard, metrics come in two varieties: those which are diagonal and hence are trivial to invert; and those which are not diagonal, and generally yield a complicated denominator upon inversion.
		An example involving the Kerr metric (a metric much-maligned for being complicated, when in fact it is still relatively simple) is used to illustrate some principles of expression management in REDTEN.
		The Kerr metric is well known in General Relativity and is identified with the vacuum solution of the Einstein Field Equations outside a spinning mass.
	www.scar.utoronto.ca /~harper/redten/node42.html (961 words)

	My Personal Reading List
		The full metric describing a Kerr fl hole in an arbitrary static and axisymmetric gravitational field is presented in a concise analytical form which allows a straightforward verification of the mass formula for fl holes.
		A sufficient condition of the regularity of the metric in the region exterior to the fl hole horizon is formulated.
		We also construct a new stationary electrovacuum metric representing binary systems of charged, magnetized, rotating, aligned masses involving one extreme object and on the basis of the numerical study oof balance equations we conjecture that the equilibrium states in such systems are impossible.
	members.localnet.com /~atheneum/bib/staxsymaps.html (4380 words)

	El espacio-tiempo completo de Kerr como modelo del espacio de la realidad física
		The Kerr metrics corresponds to a family of exact solutions of the equations of Einstein for empty field that describes fl holes with mass and with angular momentum.
		The Kerr metrics discovers a complex spacetime that can not be covered with a single coordinate system as the customarily used to cover flat spacetime.
		To deduce all the regions that exist in the complete Kerr spacetime and to obtain coordinate patches to cover these regions is the objective of analytical prolongation of the Kerr metric.
	www.ugr.es /~fran/fin3.html (4850 words)

	5.8 Kerr spacetime (Site not responding. Last check: 2007-11-05)
		Next to the Schwarzschild spacetime, the Kerr spacetime is the physically most relevant example of a spacetime in which lensing can be studied explicitly in terms of the lightlike geodesics.
		Thus, for lensing by a Kerr fl hole only the domain of outer communication is of interest unless one wants to study the case of an observer who has fallen into the fl hole.
		The literature on lightlike (and timelike) geodesics of the Kerr metric is abundant (for an overview of the pre-1979 literature, see Sharp [306]).
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2004-9/articlesu25.html (1954 words)

	Kerr metric -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-05)
		(The (Click link for more info and facts about Schwarzschild metric) Schwarzschild metric is used to describe nonrotating fl holes.) Discovered in 1963 by Roy Kerr, it is an exact solution to the (Click link for more info and facts about Einstein field equations) Einstein field equations.
		Note that r does not agree with the radial coordinate of the (Click link for more info and facts about Schwarzschild solution) Schwarzschild solution, except (Click link for more info and facts about asymptotic) asymptotically.
		The Kerr metric is not the most general cylindrically symmetric metric.
	www.absoluteastronomy.com /encyclopedia/k/ke/kerr_metric.htm (170 words)

	GRTensorII demonstrations-General Relativity & Geometry.
		The Gödel (1948) metric is of historical interest in that it provided a stimulus to the study of exact solutions of Einstein's equations.
		Demonstration 1 (kerr): An introduction to the Kerr metric: Short comparison of the time taken to show that the solution is vacuum in two coordinate systems, calculation of the Kretschmann scalar and Weyl scalars, coordinates adapted to two Killing vectors, Frobenius theorem, Ricci and Weyl scalars from a null tetrad.
		Demonstration 2 (ss2): The Einstein tensor and Kretschmann scalar are calculated for the spherically symmetric self-similar metric in comoving coordinates.
	grtensor.phy.queensu.ca /NewDemo/demo.html (1569 words)

	Preface to GKBH (Site not responding. Last check: 2007-11-05)
		Actually, the Kerr exact solution is a family of spacetimes depending on parameters m (mass) and a (angular momentum per unit mass).
		Chapter 2 establishes the basic geometry of the Kerr metric; Chapter 3 constructs maximal analytic extensions and examines their global structure; and Chapter 4 (the longest) is a detailed study of Kerr geodesics.
		A major obstacle in the vast literature on Kerr spacetime is the great variety of notational languages or formalisms that are used.
	www.math.ucla.edu /~bon/kerrpreface.html (526 words)

	Kerr Metric Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-11-05)
		Find kerr metric - Your relevant result is a click away!
		It has been suggested that Rotating fl hole be merged into this article or section.
		O'Neill, Barrett (1995) The Geometry of Kerr Black Holes, Wellesley, MA: A. Peters.
	www.karr.net /encyclopedia/Kerr_metric (1026 words)

	Kerr Black Holes, Ch.2. Beginning Kerr Spacetime (Site not responding. Last check: 2007-11-05)
		To present the Kerr metric in intuitive terms, let us picture a distant, spherically symmetric star rotating in space about a vertical axis through its center.
		When the Kerr metric is presented in terms of these familiar coordinates, they are called Boyer-Lindquist coordinates.
		A major purpose of this chapter is to extend the domain on which the Kerr metric is defined.
	www.math.ucla.edu /~bon/kerr/intro2.html (323 words)

	vallis.org: Michele's wikiblog
		Their original "hybrid" scheme was based on combining exact relativistic expressions for the evolution of the orbital elements (the semi-latus rectum p and eccentricity e) with approximate, weak-field, formula for the energy and angular momentum fluxes, amended by the assumption of constant inclination angle, iota, during the inspiral.
		The metric and curvature tensors in the field of the Sun, which were obtained in previous papers within a linearized approximation, are then calculated without this restriction.
		We find that a modest deviation from the Kerr metric is sufficient for producing a significant mismatch between the waveforms, provided we fix the orbital parameters.
	www.vallis.org /blogspace/preprints (2972 words)

	Computations in Riemann Geometry - Black Holes
		Note that this metric is the first we have considered in which curvature components with more than 2 different indices are nonzero; this is an indication of the complexity of the metric.
		First we define a function sphcart, which accepts two arguments: the dimension of a sphere, and the arguments to the sin and cos functions which will appear in the Cartesian parameterization of the unit sphere of that dimension, which is the function output.
		metric we are interested in, and define xs and xk as the coordinates of the Schwarzschild and Kerr metrics in D dimensions, respectively.
	www.rwc.uc.edu /koehler/crg/blackhole.html (2565 words)

	MAGNETOSPHERES AROUND ROTATING BLACK HOLES
		In the 1970s, a general framework was developed for constructing stationary electrovacuum Maxwell equations in the fixed background metric of the Kerr fl hole.
		It was found that aligned stationary fields are expelled out of the fl-hole horizon when its angular-momentum parameter increases, and the magnetic flux across the horizon of the maximally rotating fl hole vanishes completely in the extremely rotating case [4], [5].
		As an alternative to the approach of test fields in a pre-determined metric, exact solutions of coupled Einstein-Maxwell equations were found for certain simplified configurations: a magnetized fl hole immersed in an aligned field [8], [9], [10] is a particularly important example.
	sirrah.troja.mff.cuni.cz /~dovciak/papers/fairbank (1736 words)

	Kerr's rotating Black Holes (Site not responding. Last check: 2007-11-05)
		Roy Kerr generalized the Schwarzschild geometry to include rotating stars, and especially rotating Black Holes.
		The metric has some general properties which makes it different from the Schwarzschild metric.
		The equations of motion of particles that move along geodesics are much more complicated in the Kerr reference frame because the lack of symmetry.
	www.astro.ku.dk /~cramer/RelViz/text/geom_web/node4.html (615 words)

	Re: Questions on the Kerr metric
		>Kerr metric looks to rely only on intrisic symetry properties (ellipsoidal >instead of spherical).
		There, a nonsymmetrical tensor appears, in the metric component g_0i in the Kerr metric.
		So I do indeed find any asymmetrical g_i0 metric components very difficult too understand in a spatially rotating context.
	www.lns.cornell.edu /spr/2003-01/msg0047413.html (343 words)

	`mapfi()` (Site not responding. Last check: 2007-11-05)
		For other metrics it may be found that it is better to not evaluate the derivatives, or it may be best to fully evaluate everything from the start.
		Evaluating too soon may mean the expressions swell (especially if a sum in a denominator is formed in the metric inverse), whereas delayed evaluation may mean that many cancellations have not occurred, and a large amount of work must now be done to insert the terms.
		It is useful to turn on the showindices switch when working with an unfamiliar metric, because a judgement can then be made as to whether the calculations are proceeding at an acceptable rate, and whether a different approach might be more profitable.
	www.scar.utoronto.ca /~harper/redten/node43.html (873 words)

	[No title]
		Construction of observer's proper reference frame; spacetime metric a.
		Metric of Schwarzschild wormhole in Kruskal coordinates 2.
		Kerr fl hole as seen from outside: - frame dragging - multipole moments 3.
	www.pma.caltech.edu /Courses/ph236/public_html/outline9899.txt (1383 words)

	Bob Wagoner, Stanford Univ , ORGANIZED DISCUSSION: Are the "black hole" sources we observe described by the Kerr Metric? (Site not responding. Last check: 2007-11-05)
		Bob Wagoner, Stanford Univ, ORGANIZED DISCUSSION: Are the "fl hole" sources we observe described by the Kerr Metric?
		ORGANIZED DISCUSSION: Are the "fl hole" sources we observe described by the Kerr Metric?
		Audio for this talk requires sound hardware, and RealPlayer or RealAudio by RealNetworks.
	online.itp.ucsb.edu /online/bhole_c02/wagoner (89 words)

	Did the Big Bang Have A Cause
		Since our universe is (approximately) homogeneous and isotropic, it is described by the Robertson-Walker metric, which is determined by the radius of the universe at a given time and the curvature of space-time.
		The application of this metric to the field equations provides us with the Friedmann’s solutions, which are the heart of big bang cosmology.
		Specifically, it is possible that the vacuum solutions apply to the extent that they allow the edge of the disc formed from the collapsed star to be a white hole singularity as seen from the perspective of the spacetime into which the worldlines could be extended.
	www.qsmithwmu.com /did_the_big_bang_have_a_cause.htm (7869 words)

	Kerr holes
		The Kerr fl hole is rotating, and it is axially symmetric but not spherically symmetric.
		This solution of Einstein's equations, discovered in 1963 by R. Kerr (1963), was not at first recognized to be a fl hole solution.
		For a rotating fl hole, the Boyer-Lindquist coordinates are singular at the horizon.
	www.astro.su.se /groups/head/sara/node11.html (567 words)

	My Personal Reading List
		These will be interpreted as a `rotating Curzon metric' and a `generalised extreme Kerr metric.' In addition, approximate forms for the original metrics are given for the cases of slow rotation and small deformation.
		We present transformation formulas which facilitate the determination of the metrics, electromagnetic fields, connections and Weyl tensors of those electrovac spacetimes which result when a given solution of the Einstein-Maxwell equations with an isometry is subjected to the transformations of the Kinnersley group.
		An infinite number of infinitesimal transformations for the metric tensor preserving the equations of motion are symmarized by an explicit parametric transformation and the commutators among them are further identified to be those of the well-known Geroch group.
	members.localnet.com /~atheneum/bib/staxsym.html (14202 words)

	Modern Trends in String Theory II (Site not responding. Last check: 2007-11-05)
		We give the general Kerr-de Sitter metric in arbitrary spacetime dimension D >= 4, with the maximal number (D-1)/2 of independent rotation parameters.
		We obtain the metric in Kerr-Schild form, where it is written as the sum of a de Sitter metric plus the square of a null geodesic vector, and in generalised Boyer-Lindquist coordinates.
		All previously-known cases, supersymmetric and non-supersymmetric, that have equal angular momenta are encompassed as special cases.
	www.math.ist.utl.pt /~strings/MTST2/pope2.html (133 words)

	News at UCD, March 2001
		The Einstein equations are then derived in terms of this “metric”, of the conformal extrinsic curvature and in terms of the associated derivative.
		We apply this method to the problem of orbit motion of test particles in Schwarzschild and Kerr metrics; from a simple circular orbit as the initial geodesic we obtain finite eccentricity orbits as a Taylor series with respect to the eccentricity.
		Since, for arbitrary N, the superenergy of any simple form is a self-map of the cone (its square is proportional to the metric) this leads to new representations and classifications of all conformal Lorentz transformations and to generalisations of the Rainich-Misner-Wheeler theory of determining the space-time physics from its geometry.
	www.ucd.ie /news/mar01/abstracts.htm (4715 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		Investigation of general relativistic (GR) accretion flows in Kerr metric may provide an important step towards a better understanding of this problem.
		Also, it might be instructive to study the properties of matter around a spinning (Kerr) BH to have a more realistic understanding of how matter dives onto stellar mass and super-massive BHs and what could be the its possible consequences.
		Sound propagation is described by an acoustic metric algebraically dependent on the flow density and Mach number; which is conformaly related to the Painleve
	www.mri.ernet.in /~tapas/future_research/future_research.html (1733 words)

	Uniqueness of the Newman-Janis algorithm in generating the Kerr-Newman metric (Site not responding. Last check: 2007-11-05)
		After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be ``derived'' by making an elementary complex transformation to the Schwarzschild solution.
		Contrary to this belief this paper shows why the Newman-Janis algorithm is successful in obtaining the Kerr-Newman metric by removing some of the ambiguities present in the original derivation.
		Finally we show that the only perfect fluid generated by the Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric.
	www.physics.adelaide.edu.au /mathphysics/abstracts/ADP-98-41-M70.html (196 words)

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