
	Where results make sense

Topic: No hair theorem

Related Topics

Black hole

In the News (Thu 17 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	No hair theorem - Wikipedia, the free encyclopedia
		In astrophysics, the no-hair theorem states that fl holes are completely characterized only by three externally observable parameters: mass, electrical charge, and angular momentum.
		The no-hair theorem was originally formulated for fl holes within the context of a four-dimensional spacetime, obeying the Einstein field equation of general relativity with zero cosmological constant, in the presence of electromagnetic fields (or optionally other fields such as scalar fields, massive vector fields (Proca fields), spinor fields, etc.).
		Counterexamples in which the theorem fails are known in spacetime dimensions higher than four; when the cosmological constant is nonzero; in the presence of nonabelian Yang-Mills fields, nonabelian Proca fields, some non-minimally coupled scalar fields, or skyrmions; or in some theories of gravity other than Einstein's general relativity.
	en.wikipedia.org /wiki/No_hair_theorem (402 words)

	Hair
		Hair Hair is also a Hair (musical) Hair is most commonly that outgrowth of the trichomes (see for further discussion of...
		Hair of the dog The phrase "Hair of the Dog" is used to refer to a drug consumed with the intent of lessening or postpon...
		Leg hair Leg hair is hair that grows on the legs of humans, generally appearing at the onset of adulthood.
	www.brainyencyclopedia.com /topics/hair.html (431 words)

	[No title]
		Their form agrees with the predictions of the proposal that the universe has no boundaries or edges in the imaginary time direction; but further observations will be necessary to distinguish this proposal from other possible explanations for the fluctuations in the background.
		No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory.
		We have no direct evidence as to whether the matter in other galaxies is made up of protons and neutrons or antiprotons and anti-neutrons, but it must be one or the other: there cannot be a mixture in a single galaxy because in that case we would again observe a lot of radiation from annihilations.
	www.geocities.com /picturesref/time.html (24318 words)

	No hair theorem
		It should be noted, however, that not all theoreticians believe that the "no hair" holds completely.
		For example, Penrose argues that at least some of the information "lost" at the event horizon will be recovered during the process of fl hole evaporation.
		Hawking says the problem with the no hair theorem is that it implies the fl hole will emit the same radiation regardless of what goes into the fl hole.
	www.sciencedaily.com /encyclopedia/no_hair_theorem (286 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		This was then generalized to the no hair theorem, the only stationary rotating fl hole solutions of the Einstein Maxwell equations, are the Kerr Newman metrics.
		The no hair theorem implied that all information about the collapsing body, was lost from the outside region, apart from three conserved quantities, the mass, the angular momentum, and the electric charge.
		No one has found a mechanism to produce correlations, but most physicists believe one must exist.
	pancake.uchicago.edu /~carroll/hawkingdublin.txt (2582 words)

	Stephen Hawking - Wikipedia, the free encyclopedia
		In 1981, Hawking proposed that, although the universe had no boundary, it was finite in space-time; 1983 saw his mathematical proof of this theory.
		Classically, it can be shown that information crossing the event horizon of a fl hole is lost to our universe, and that as a consequence all fl holes are identical, beyond their mass, electrical charge and angular velocity (the "no hair theorem").
		The problem with this theorem is that it implies the fl hole will emit the same radiation regardless of what goes into the fl hole, and as a consequence that if a pure quantum state is thrown into a fl hole, an "ordinary" mixed state will be returned.
	en.wikipedia.org /wiki/Stephen_Hawking (2567 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		This conclusion, known as the theorem "A fl hole has no hair," was proved by the combined work of Carter, Werner Israel of the University of Alberta, David C. Robinson of King's College, London, and me. The no-hair theorem implies that a large amount of information is lost in a gravitational collapse.
		Yet according to classical concepts no such equilibrium is possible, since the fl hole would absorb any thermal radiation that fell on it but by definition would not be able to emit anything in return.
		The reason a fl hole "remembers" the electric charge, angular momentum and mass of the matter that collapsed and "forgets" everything else is that these three quantities are coupled to long-range fields: in the case of charge the electromagnetic field and in the case of angular momentum and mass the gravitational field.
	www.grahamkendall.net /Unsorted_files-2/A319-Hawking's_Quantum.txt (3925 words)

	Physics 776, Fall 2003
		Hawking's original area theorem proved that if the null energy holds, and if the horizon generators extend to infinite affine parameter (a no-singularity condition), then the expansion of the horizon-generating congruence cannot be negative anywhere.
		A proof of the area theorem that doesn't assume smoothness of the horizon was given fairly recently by Chrusciel et al.
		no hair theorem): This was initially quite surprising to many people, who thought that somehow the multipole moments would be frozen in as an asymmetric object collapsed through an event horizon.
	www.physics.umd.edu /grt/taj/776b/notes.html (7230 words)

	Stephen Hawking (Site not responding. Last check: 2007-10-13)
		In 1981, Hawking proposed that although the universe has no boundary, it is finite in space-time, and in 1983 he proved this mathematically.
		This is known as the no hair theorem.
		The problem with the no hair theorem is that it implies the fl hole will emit the same radiation regardless of what goes into the fl hole.
	www.worldhistory.com /wiki/S/Stephen-Hawking.htm (1935 words)

	On the existence of conformally coupled scalar field hair for black holes in (anti-)de Sitter space (Site not responding. Last check: 2007-10-13)
		The theorem relies on the assumption that the weak energy condition is satisfied by the matter fields, i.e.
		It is by no means clear whether this is a reasonable expectation for our system, given not only the non-minimal coupling of matter to the geometry, but also the presence of a negative cosmological constant.
		R-G. Cai and J-Y. Ji, “Hairs on the cosmological horizon”.
	www.shef.ac.uk /~ap1ew/bekenstein/conformal.html (7237 words)

	Michael Nielsen » Blog Archive » The Planck length
		If you take the “no hair” theorem of general relativity seriously, then you’d believe that such a fl hole should have no internal structure.
		Nonetheless, this argument does seem suggestive that particle having wavefunctions with structure on the Planck scale would, indeed, be very interesting objects, and that it is at least somewhat likely that general relativity, quantum mechanics, or both, would break down at that level.
		There is no need to think about the source as a single particle wave-function, rather it is about whatever constitutes the energy momentum tensor.
	www.qinfo.org /people/nielsen/blog?p=205 (1347 words)

	No possibility \| Samizdata.net
		In the 70s, Hawking proved the "No-Hair Theorem" which states that a stationary fl hole is completely specified by it mass, electric charge and angular momentum.
		In the standard model of particle physics, there are several quantities which must be conserved, for example, "baryon number" which is the number of protons plus the number of neutrons, minus the number of anti-protons minus the number of anti-neutrons.
		As long as no resources are coerced from individuals in funding 'research' I ulitmately don't care.
	www.samizdata.net /blog/archives/006420.html (3208 words)

	To baldly go where no man went before \| The String Coffee Table
		Posted by Robert H. In his reference frame, Lubos reports on a seminar by Reall on higher dimensional fl holes and fl rings and mentions that they violate a possible no hair theorem.
		Is the no hair theorem just a coincidence of a small class of theories or does it have a fundamental meaning or relevance (as for example cosmic censorship, a violation of which would have bad consequences for predictability)?
		Is the no hair theorem just a coincidence of a small class of theories or does it have a fundamental meaning or relevance […]?
	golem.ph.utexas.edu /string/archives/000508.html (528 words)

	Singularities and Black Holes, CARM
		One might dump the Encyclopedia Britannica into a fl hole, for example, and the "no hair" theorem suggests that all of the organized information in that set of books would be lost to external observers for all time.
		Mass/energy at the most basic level is characterized by several "quantum numbers" or "characteristics", and the "no hair" theorem implies that much of the information about even individual particles is lost when they enter the event horizon.
		In a sense this doesn't matter, because once the infalling observer crosses the EH two things occur: (1) s/he an no longer communicate anything to the distant, "fixed" observer, and (2) s/he is doomed to encounter the singularity at some point, since within the event horizon all world lines (geodesics) lead to the singularity.
	www.carm.org /evolution_archive/singularities.htm (2383 words)

	5.4 Newtonian cosmology (Site not responding. Last check: 2007-10-13)
		This is no less true for existence theorems than for other issues.
		The first[9] is an analogue of the cosmic no hair theorem (cf.
		The third[63] says that the homogeneous and isotropic models in Newtonian cosmology which correspond to a k =-1 Friedmann-Robertson-Walker model in general relativity are non-linearly stable.
	relativity.livingreviews.org /Articles/lrr-1998-4/node18.html (250 words)

	COURSE NOTES - ASTRO 102/112, Part 12 (Site not responding. Last check: 2007-10-13)
		There is no "wall" at the event horizon that says "beware ye who enter here..." in fact you notice nothing special as you pass inside the event horizon!
		No legitimate solution to Einstein's equations has ever been found which allows you to return to the same place at an earlier time (and of course nothing in experiment, never mind theory).
		In other words, they have no details or individuality apart from their size, spin, and perhaps charge.
	www.astro.lsa.umich.edu /users/garyb/Course/WWW/Notes/notes12.html (4633 words)

	Almost Hairless \| Musings
		To no one’s great surprise, but to the consternation of some, the flhole no-hair theorem does not hold in higher dimensions.
		In four dimensions, flhole solutions are characterized by their gauge charges: mass, angular momentum, electric charge, … (and perhaps discrete gauge charges, should there be discrete factors in the gauge group).
		Bena and Warner found a rich class of supersymmetric fl ring solutions which seem to comprise an infinite amount of (continuous) “hair.” Their solutions are characterized by seven functions of one variable, the position along a curve,
	golem.ph.utexas.edu /~distler/blog/archives/000481.html (320 words)

	sciforums.com - The implications of ThermoDynamics on Black Holes
		According to general relativity, gravity is a manifestation of the curvature of spacetime so, at the singularity of a fl hole (r=0) the curvature is infinite.
		The no hair theorem simply states that mass, charge and angular momentum are the only properties a fl hole possesses.
		There is no known physical mechanism that can explain how such an object would not succumb to gravity and collapse to a singularity.
	www.sciforums.com /showthread.php?t=13286 (1424 words)

	Physics 675, Fall 2004
		No observer can pass through the wormhole: once at r=1 any timelike observer must proceed to smaller values of r.
		Since nothing can get out of a fl hole, the radiation can carry no information, it must have a maximum entropy, reflecting only the aspects of the fl hole that can be seen on the outside: mass, angular momentum and charge if the hole is charged.
		Hence if there are no timelike tangent vectors n.s must vanish for all vectors s in the surface.) Since the null vector is also orthogonal to itself, it is orthogonal to all vectors in the surface, i.e.
	www.physics.umd.edu /grt/taj/675a/notes.html (10113 words)

	Research (Site not responding. Last check: 2007-10-13)
		This conjecture - called ``no-hair'' theorem - was proved rigorously in some cases, but not in general.
		Surprisingly, it turned out that the ``no-hair'' theorem is not valid, if the Black Hole is coupled to fields with non-linear interactions.
		The investigation of the fl holes with ``hair'' promisses exciting new results and a deeper understanding of gravity.
	www.physik.uni-oldenburg.de /Docs/ftheorie/researchbk.html (376 words)

	Information Paradox solution by Hawking (loses bet), 2004 :: Web development and technology forum. (Site not responding. Last check: 2007-10-13)
		Otherwise, energy can be created or destroyed and that is a contradiction of one of the fundamental rules of quantum mechanics, which is the conservation of energy.
		If all fl holes are the same, then no fl hole can be traced back to its unique beginning, and any information about the particles that created it is lost forever at the moment the hole forms.
		But finally it Hawking has conceded that, the Hawking Radiation that escapes from the boundry of the event horizon emits particles and therefore the fl hole suffers a loss to both mass and energy.
	www.dna88.com /forum/viewtopic.php?t=323-53k (3699 words)

	I have no lover, and she hasn't the prettiest eyes. (Site not responding. Last check: 2007-10-13)
		I have no lover, and she hasn't the prettiest eyes.
		The no hair theorem was extended by Robinson to the case
		This is the singularity that the Hawking-Penrose theorem predicts.
	www.livejournal.com /~westaredsolong (10278 words)

	Homework 6 Discussion (Site not responding. Last check: 2007-10-13)
		Eventually the last signal will be sent and the probe will be heard from no more as the reshift and time dilation head toward infinity.
		Further, if the gravitational field doesn't change, there is no gravitational radiation, no gravity waves produced.
		The No Hair Theorem tells us that the fl hole horizon cannot stay in a nonspherical state, but must radiate gravitational waves until it becomes spherical.
	www.astro.virginia.edu /~jh8h/astr348/h6info.html (695 words)

	A Brief History of The Concept of Gravitational Collapse (Site not responding. Last check: 2007-10-13)
		This theorem shows that the singularities which had been found in exact solutions such as the Schwarzschild, Reissner-Nordstrom, and Kerr solutions are not artifacts of the idealized symmetry of these solutions.
		In 1973, Jacob Beckenstein suggests the intriguing similarity of Hawking's area theorem and the Second Law of Thermodynamics is no coincidence, and proposes that the area of the event horizon of a fl hole must somehow represent its entropy.
		Meanwhile, Robinson proves the No Hair Theorem: the exterior region of a rotating charged isolated fl hole must be described by the exterior region of the Kerr-Newman solution.
	math.ucr.edu /home/baez/RelWWW/history.html (7117 words)

	Citebase - Inflation in Bianchi models and the cosmic no hair theorem in brane world (Site not responding. Last check: 2007-10-13)
		Authors: Paul, B. In this paper, the cosmic no hair theorem for anisotropic Bianchi models which admit inflation with a scalar field is studied in the framework of Brane world.
		The Cosmic no hair theorem is studied in anisotropic Bianchi brane models which admit power law inflation with a scalar field.
		We derive a set of sufficient conditions which must be satisfied by the brane matter and bulk metric so that a homogeneous and anisotropic brane asymptotically evolves to a de Sitter spacetime in the presence o...
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/0204089 (1210 words)

	PROGRAM IN GENERAL RELATIVITY (Site not responding. Last check: 2007-10-13)
		These courses are topically oriented in which the prinicipal ideas / results are carefully described, with the routine calculations being outlined, but not repeated if they are readily available in the usual texts.
		There are no written examinations, and grading is based on problem sets that are due at regular intervals.
		The elementary theory of degenerate stars; physics of gravitational collapse; derivations of the axially symmetric solutions of Weyl, Kerr, and Validya; the Penrose process and Hawking's area theorem; the 'no hair' theorem; Penrose's cosmic censorship conjecture; Hawking radiation; and the observational evidence for fl holes.
	www.math.nmsu.edu /jdz/generalrelativity.html (400 words)

Try your search on: Qwika (all wikis)