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Topic: Schwarzschild metric

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	Schwarzschild metric - Wikipedia, the free encyclopedia
		In Einstein's theory of general relativity, the Schwarzschild solution (or the Schwarzschild vacuum) describes the gravitational field outside a spherical, non-rotating mass such as a (non-rotating) star, planet, or fl hole.
		The Schwarzschild solution is named in honour of its discoverer Karl Schwarzschild who found the solution in 1916, only a few months after the publication of Einstein's theory of general relativity.
		The Schwarzschild fl hole is characterized by a surrounding area, called the event horizon which is situated at the Schwarzschild radius, often called the radius of a fl hole.
	en.wikipedia.org /wiki/Schwarzschild_metric (1332 words)

	Deriving the Schwarzschild solution - Wikipedia, the free encyclopedia
		The Schwarzschild solution is one of the simplest and useful solutions of the Einstein field equations (see general relativity).
		It is worthwhile deriving this metric in some detail; the following is a reasonably rigorous derivation that is not always seen in the textbooks.
		In deriving the Schwarzschild metric, it was assumed that the metric was vacuum, spherically symmetric and static.
	en.wikipedia.org /wiki/Deriving_the_Schwarzschild_solution (679 words)

	My Personal Reading List
		This metric is asymptotically flat and describes correctly the exterior gravitational field of a magnetized spinning mass.
		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.
	members.localnet.com /~atheneum/bib/staxsymaps.html (4380 words)

	Very Strong Gravity (Site not responding. Last check: 2007-11-07)
		Notice that the metric is in spherical coordinates, t, r(radius from the origin), theta and phi.
		At the Schwarzschild radius the escape velocity is the speed of light.
		For the Earth the Schwarzschild radius is 9 millimeters.
	www.geocities.com /CapeCanaveral/Hall/5803/grav.html (458 words)

	Talk:Schwarzschild metric - Wikipedia, the free encyclopedia
		I've taken out a chunk of this article and extended it to give a more detailed derivation of the Schwarzschild metric in deriving the Schwarzschild solution (for those interested in such things).
		In other articles where this metric is mentioned, I agree that putting c=1 is ok, as long as this is stated (like in some of the GR articles).
		If you have questions about how the Schwarzschild metric and aspects of general relativity (like the mass/energy equivalence) relate to each other, a suitable place to discuss this is either on this talk page, or at Talk:General relativity).
	en.wikipedia.org /wiki/Talk:Schwarzschild_metric (827 words)

	Schwarzschild Geometry
		Curiously, the Schwarzschild radius had already been derived (with the correct result, but an incorrect theory) by John Michell in 1783 (this reference is from Erk's Relativity Pages) in the context of Newtonian gravity and the corpuscular theory of light.
		The Schwarzschild geometry is illustrated in the embedding diagram at the top of the page, which shows a 2-dimensional representation of the 3-dimensional spatial geometry at a particular instant of universal time t.
		The problem with the Schwarzschild metric is that it describes the geometry as measured by observers at rest.
	casa.colorado.edu /~ajsh/schwp.html (2298 words)

	Sperical metrics (Site not responding. Last check: 2007-11-07)
		Spherical metrics are not only of interest in the present context for the description of the universe at cosmological scales, but also as descriptions of fl holes and of the metric around any source of matter at large distances (the orbit of a planet around a star, etc.).
		However, in the derivation of the Schwarzschild metric one does not have to constrain the mass distribution that gives rise to it as static; it merely has to remain spherically symmetric.
		Apart from the Schwarzschild metric, which is useful to describe the effect of localized mass distributions at large distances and spherically symmetric distributions in empty regions, we would like to discuss the Robertson-Walker metric.
	www.nikhef.nl /~henkjan/astro/node17.html (1092 words)

	White Holes and Wormholes
		The Schwarzschild metric admits negative square root as well as positive square root solutions for the geometry.
		The trapped region between the two horizons is the Schwarzschild bubble encountered on the trip into the fl hole.
		We are at 0.35 Schwarzschild radii from the central singularity.
	casa.colorado.edu /~ajsh/schww.html (1197 words)

	ipedia.com: Black hole Article (Site not responding. Last check: 2007-11-07)
		The Schwarzschild radius is now known to be the radius of a fl hole, but was not well understood at that time.
		General relativity (as well as most other metric theories of gravity) not only says that fl holes can exist, but in fact predicts that they will be formed in nature whenever a sufficient amount of mass gets packed in a given region of space, through a process called gravitational collapse.
		For an object with the mass of the Earth, the Schwarzschild radius is a mere 9 millimeters — about the size of a marble.
	www.ipedia.com /black_hole.html (3562 words)

	[No title]
		This metric describes a time like interval with dr =0 and d{\f1 f}=0 on a fixed radial shell as observed by a far away observer.
		If you compressed the sun down to a radius of 3 kilometers, it would also form a fl hole.\par \par The singularity in the metric at the Schwarzschild radius, r=2*M, is nonessential and can be removed by a coordinate transform, but the singularity at r=0 is real and can not be transformed away.
		This formula was derived from the Schwarzschild metric with dr=0 for both objects and circular orbits.
	home.earthlink.net /~rrs0/Schwarzschild/Schwarzschild.mcd (1032 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].
		(In this paper the authors constantly refer to their interior metric as to a “dust” where obviously a perfect fluid with constant density is meant.) Effects on light rays issuing from the star’s interior have been discussed already earlier by Lawrence [203].
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2004-9/articlesu18.html (2796 words)

	Spacetime Geometry Inside a Black Hole
		The Schwarzschild metric was derived using the reference frame in which the fl hole is stationary.
		This means that the coefficients of the Schwarzschild metric are valid for observers “at rest” in the gravitational field of the fl hole.
		We found earlier that the Schwarzschild metric has a coordinate singularity at the event horizon, where an outside observer measures an infalling observer’s time to be approaching infinity as he approaches the event horizon (infinite redshift).
	members.cox.net /jhaldenwang/black_hole.htm (5304 words)

	A Flaw of General Relativity, a New Metric and Cosmological Implications
		A new metric for Schwarzschild geometry is derived and shown to be confirmed by all experimental tests of the Schwarzschild metric.
		The velocity given by Newton’s equation is c (unity) at the Schwarzschild radius R (at r / R = 1) and approaches a limit of infinity (shown truncated at 2c) as r approaches a limit of zero.
		Then, for example, the new metric predicts that the relativistic orbital precession for Mercury is 42.98 arc seconds per century, the same as the Schwarzschild metric predicts.
	zanket.home.att.net (4032 words)

	FAQ to SCI.PHYSICS on Black Holes by Matt McIrvin
		The metric is a formula that may be used to obtain the "length" of a curve in spacetime.
		Schwarzschild expressed his metric in terms of coordinates which, at large distances from the object, resembled spherical coordinates with an extra coordinate t for time.
		Therefore the fatal r goes as the cube root of the mass, whereas the Schwarzschild radius of the fl hole is proportional to the mass.
	antwrp.gsfc.nasa.gov /htmltest/gifcity/bh_pub_faq.html (3321 words)

	Schwarzschild Metric - Part 2 (Site not responding. Last check: 2007-11-07)
		The metric has a form due to spherical symmetry however that allows us to do a transformation that completely removes this time dependence.
		Metrics like this, which are also stationary, are called static.
		We have shown that the most general spherically symmetric metric is such that all time dependence of the gravitational field can be transformed away.
	scholar.uwinnipeg.ca /courses/38/4500.6-001/Cosmology/Schwarzschild_Metric2.htm (483 words)

	General Relativity.
		The so-called "Schwarzschild" solution is due to David Hilbert, itself a corruption of a solution first derived by Johannes Droste in May 1916, whose paper has also been buried or ignored at the convenience of the experts.
		Schwarzschild's paper is a piece of flawless mathematical physics, but Hilbert's is a poor show.
		I show that r is neither a radius nor a coordinate in the gravitational field and is in fact only a real-valued parameter, and that the proper radius and the radius of curvature, both functions of r, and which are not the same, are the relevant radial quantities in Einstein's gravitational field.
	www.geocities.com /theometria (1891 words)

	Not-So-Cosmic Censorship and Black Holes
		Equivalents of the Schwarzschild metric that are static and that do not exhibit fl holes are presented for the first time and discussed.
		The metric is analogous to an expression for the hypotenuse of a right triangle, generalized to four dimensions, in that it expresses the “distance” between two neighboring event points in terms of four coordinate components.
		It is the threat that the rising mountain of literature in the field will bury any essential elements that have been earlier overlooked, should they fail to support the dominant schools of thought at the top.
	www.angelfire.com /empire/intensity/brunstein.htm (2782 words)

	Maxima Manual: 29. ctensor (Site not responding. Last check: 2007-11-07)
		As an example, consider a simple metric that is a perturbation of the Minkowski metric.
		The null tetrad is constructed on the assumption that a four-diemensional orthonormal frame metric with metric signature (-,+,+,+) is being used.
		Changing to a frame base at a later stage could yield inconsistent results, as you may end up with a mixed bag of tensors, some computed in a frame base, some in a coordinate base, with no means to distinguish between the two.
	maxima.sourceforge.net /docs/manual/en/maxima_29.html (2290 words)

	ilovephysics.com :: Free online physics help, tutorials, forum, and cool stuff / A Flaw of General Relativity, a Fix, ...
		The predictions of the new metric are shown to diverge from those of the Schwarzschild metric as gravity strengthens.
		Until then, the Kerr metric could still be used as an approximation, where it is more accurate (better matches observation) than the new metric for Schwarzschild geometry in the paper.
		The fix of GR in the paper is the new metric for Schwarzschild geometry (a fix is by definition a temporary solution).
	www.ilovephysics.com /forum/viewtopic.php?pid=684 (3175 words)

	Distortions Paper Principles and Mathematics
		Einstein's general relativity [15] is not the only gravitational theory that admits the Schwarzschild metric as an exterior solution for a spherically symmetric, non-rotating gravitational field, but it is the preferred theory, and the theory that will be assumed implicitly here.
		Here ds is a metric measure of coordinate distance r, coordinate time t and coordinate angles theta and phi.
		The term R_S, the Schwarzschild radius, refers to the radius of a fl hole event horizon, and c refers to the local speed of light.
	antwrp.gsfc.nasa.gov /htmltest/gifcity/nslens_math.html (992 words)

	The Present Invalid Nature of Humphreys' White Hole Cosmology
		Outside the sphere, the metric has to be the same as the Schwarzschild metric, eq.
		Based upon Humphreys' Schwarzschild exterior geometry, this value appears, at the least, to be required during the entire day four and, probably, through day six so that the event horizon (Schwarzschild surface) remains approximately at the earth's surface.
		Thus, assuming that there is an event horizon at the earth's surface that is produced by the collapse of an event horizon at the outer boundary yields, for this metric, a cosmological constant that when applied to the entire universe does not yield the required event horizon at the outer boundary.
	www.serve.com /herrmann/hump.htm (787 words)

	Schwarzschild holes
		The Schwarzschild fl hole is named after Karl Schwarzschild, who in 1916 derived the relativistic solution for the gravitational field surrounding a nonrotating, electrically neutral sphere.
		The Schwarzschild metric is a vacuum solution of Einstein's field equations, it is valid only in the empty space outside the object.
		The mathematical form of the metric is different in the object's interior, and will not be discussed here.
	www.astro.su.se /Xgamma/sara/node10.html (462 words)

	ProjectCalculus
		The Schwarzschild metric is a differential equation providing a solution to Einstein's field equations of General Relativity.
		The metric was discovered by the German physicist, Karl Schwarzschild, and it describes space and time in the vicinity of a fl hole.
		One familiar metric is the Pythagorean theorem, which provides a measure of the hypotenuse of a right triangle given the lengths of the two sides.
	shell.amigo.net /~rdorsett/ProjectCalculus/ProjCalc.htm (423 words)

	Flying Clocks (Site not responding. Last check: 2007-11-07)
		To this point we have neglected the gravitational field of the Earth by assuming that the metric of spacetime was the flat Minkowski metric.
		We saw in Section 6.4 that the metric in the equatorial plane of a spherical gravitating body of mass m at a constant Schwarzschild radial parameter r from the center of that body is
		One way of approaching a problem such as this is to work with the Schwarzschild metric expressed in terms of "orthogonal" quasi-Minkowskian coordinates.
	www.mathpages.com /rr/s6-06/6-06.htm (1539 words)

	Classical Unified Force
		Under weak, static conditions, the unified metric is a good approximation of the Schwarzschild metric of general relativity.
		A metric is a function that involves differential elements of time, space and the interval.
		The first term of the force is the one that leads to an approximation of the Schwarzschild metric, and by extension, Newton's law of gravity.
	world.std.com /~sweetser/arch/unified_force.2001.09.01/unified_force.html (1994 words)

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