Showing posts with label Black Holes. Show all posts
Showing posts with label Black Holes. Show all posts

Wednesday, February 17, 2016

No-Hair Theorem

The no-hair theorem postulates that all black hole solutions of the Einstein-Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three externally observable classical parameters: mass, electric charge, and angular momentum.[1] All other information (for which "hair" is a metaphor) about the matter which formed a black hole or is falling into it, "disappears" behind the black-hole event horizon and is therefore permanently inaccessible to external observers. Physicist John Archibald Wheeler expressed this idea with the phrase "black holes have no hair"[1] which was the origin of the name. In a later interview, John Wheeler says that Jacob Bekenstein coined this phrase.[2]

The first version of the no-hair theorem for the simplified case of the uniqueness of the Schwarzschild metric was shown by Werner Israel in 1967.[3] The result was quickly generalized to the cases of charged or spinning black holes.[4][5] There is still no rigorous mathematical proof of a general no-hair theorem, and mathematicians refer to it as the no-hair conjecture. Even in the case of gravity alone (i.e., zero electric fields), the conjecture has only been partially resolved by results of Stephen Hawking, Brandon Carter, and David C. Robinson, under the additional hypothesis of non-degenerate event horizons and the technical, restrictive and difficult-to-justify assumption of real analyticity of the space-time continuum.




Suppose two black holes have the same masses, electrical charges, and angular momenta, but the first black hole is made out of ordinary matter whereas the second is made out of antimatter; nevertheless, they will be completely indistinguishable to an observer outside the event horizon. None of the special particle physics pseudo-charges (i.e., the global charges baryonic number, leptonic number, etc.) are conserved in the black hole.[citation needed]

Changing the reference frame
Every isolated unstable black hole decays rapidly to a stable black hole; and (excepting quantum fluctuations) stable black holes can be completely described (in a Cartesian coordinate system) at any moment in time by these eleven numbers:
These numbers represent the conserved attributes of an object which can be determined from a distance by examining its gravitational and electromagnetic fields. All other variations in the black hole will either escape to infinity or be swallowed up by the black hole.
By changing the reference frame one can set the linear momentum and position to zero and orient the spin angular momentum along the positive z axis. This eliminates eight of the eleven numbers, leaving three which are independent of the reference frame. Thus any black hole which has been isolated for a significant period of time can be described by the Kerr–Newman metric in an appropriately chosen reference frame.

Four-dimensional space-time

The no-hair theorem was originally formulated for black 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 and massive vector fields (Proca fields, spinor fields, etc.).[citation needed]


It has since been extended to include the case where the cosmological constant is positive (which recent observations are tending to support).[6]
Magnetic charge, if detected as predicted by some theories, would form the fourth parameter possessed by a classical black hole.


Counterexamples in which the theorem fails are known in spacetime dimensions higher than four; in the presence of non-abelian Yang-Mills fields, non-abelian Proca fields, some non-minimally coupled scalar fields, or skyrmions; or in some theories of gravity other than Einstein’s general relativity. However, these exceptions are often unstable solutions and/or do not lead to conserved quantum numbers so that "The 'spirit' of the no-hair conjecture, however, seems to be maintained".[7] It has been proposed that "hairy" black holes may be considered to be bound states of hairless black holes and solitons.
In 2004, the exact analytical solution of a (3+1)-dimensional spherically symmetric black hole with minimally coupled self-interacting scalar field was derived.[8] This showed that, apart from mass, electrical charge and angular momentum, black holes can carry a finite scalar charge which might be a result of interaction with cosmological scalar fields such as the inflaton. The solution is stable and does not possess any unphysical properties, however, the existence of scalar field with desired properties is only speculative.

Observational results

The LIGO results provide the first experimental observation of the uniqueness or no-hair theorem.[9][10] This observations are consistent with Stephen Hawking theoretical work on black holes in the 1970s.[11][12]

See also


  • Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald (1973). Gravitation. San Francisco: W. H. Freeman. pp. 875–876. ISBN 0716703343. Retrieved 24 January 2013.
  • Israel, Werner (1967). "Event Horizons in Static Vacuum Space-Times". Phys. Rev. 164 (5): 1776–1779. Bibcode:1967PhRv..164.1776I. doi:10.1103/PhysRev.164.1776.
  • Israel, Werner (1968). "Event horizons in static electrovac space-times". Commun. Math. Phys. 8 (3): 245–260. Bibcode:1968CMaPh...8..245I. doi:10.1007/BF01645859.
  • Carter, Brandon (1971). "Axisymmetric Black Hole Has Only Two Degrees of Freedom". Phys. Rev. Lett. 26 (6): 331–333. Bibcode:1971PhRvL..26..331C. doi:10.1103/PhysRevLett.26.331.
  • Bhattacharya, Sourav; Lahiri, Amitabha (2007). "No hair theorems for positive Λ". arXiv:gr-qc/0702006v2.
  • Mavromatos, N. E. (1996). "Eluding the No-Hair Conjecture for Black Holes". arXiv:gr-qc/9606008v1.
  • Zloshchastiev, Konstantin G. (2005). "Coexistence of Black Holes and a Long-Range Scalar Field in Cosmology". Phys. Rev. Lett. 94 (12): 121101. arXiv:hep-th/0408163. Bibcode:2005PhRvL..94l1101Z. doi:10.1103/PhysRevLett.94.121101.
  • "Gravitational waves from black holes detected". BBC News. 11 February 2016.
  • "Gravitational waves detected 100 years after Einstein's prediction" (PDF). LIGO. February 11, 2016. Retrieved 11 February 2016.
  • Stephen Hawking

    1. Stephen Hawking celebrates gravitational wave discovery

    External links


  • Black holes
  • Theorems in general relativity
  • Sunday, October 19, 2014

    Black Holes, String Theory and the Fundamental Laws of Nature with Andrew Strominger

    What are black holes? What are they made of? What is string theory? Is everything we see just vibrations of strings? How are string theory and black holes related? What are the fundamental laws of Nature?
    For decades, since the discovery of quantum mechanics and Einstein’s theory of relativity, scientists have been trying to combine the two perspectives of the world into one single unified theory. One of the results was string theory: where the strangeness of quantum reality and the weirdness of relativity theory come together and create something even more puzzling - a world with extra dimensions
    String theory says that there is only one fundamental object in the universe: the string. Much like the strings in a guitar give rise to different sounds when you pluck them, the strings of string theory give rise to the different constituents of the observed reality when you make them vibrate at different energies. Is everything in the world made of strings? If so, what is a black hole? SEE:
     Black Holes, String Theory and the Fundamental Laws of Nature with Andrew Strominger

    Wednesday, June 25, 2014

    Black holes, quantum information, and the foundations of physics

    Volume 66, Issue 4, April 2013

    Quantum mechanics teaches that black holes evaporate by radiating particles—a lesson indicating that at least one pillar of modern physics must fall. See: Black holes, quantum information, and the foundations of physics by Steven B. Giddings, in Physics Today, April 2013

    Based on an image from NASA/CXC/M.Weiss
    Citation: Phys. Today 66, 4, 30 (2013);
    image of Untitled

    of the Schwarzschild black hole solution can be depicted in different ways. In this representation, ingoing light rays always travel along ingoing lines heading toward the top and left at 45°; outgoing light rays asymptotically approach 45° lines at large radius . Massive particles, with their slower speeds, must travel within the light cones (blue) between outgoing and ingoing light rays, as illustrated by the red path. No light ray can escape to infinity from inside the vertical dotted line, the horizon located at the mass-dependent Schwarzschild radius (). Instead, any trajectory beginning inside the horizon is pulled to a central point, the singularity at = 0, where spacetime curvature becomes infinite.
    Citation: Phys. Today 66, 4, 30 (2013);

    Saturday, September 07, 2013

    Catching Black Holes on the Fly

    Black Holes Shine for NuSTAR Image Credit: NASA/JPL-Caltech
    NASA's black-hole-hunter spacecraft, the Nuclear Spectroscopic Telescope Array, or NuSTAR, has "bagged" its first 10 supermassive black holes. The mission, which has a mast the length of a school bus, is the first telescope capable of focusing the highest-energy X-ray light into detailed pictures. See: Catching Black Holes on the Fly


    Thursday, August 29, 2013

    How to Find Black holes with Lasers

    In February 2013 I was invited by the Institute of Physics to give a lecture in the famous lecture theatre of the Royal Institution of Great Britain as part of their Physics in Perspective series. I was to expect about 400 students and teachers from schools across the country. See: How to Find Black holes with Lasers


    Friday, August 16, 2013

    NuStar: Blackhole Hunter

    NuSTAR is opening a new window on the Universe by being the first satellite to focus high-energy X-rays into sharp images. NuSTAR’s high-energy X-rays eyes see with more than 100 times the sensitivity of previous missions that have operated in this part of the electromagnetic spectrum, and with 10 times better resolution. NuSTAR sheds light on some of the hottest, densest, and most energetic objects in the universe.Education & Outreach

    Black Hole Websites

    See Also:

    Thursday, August 08, 2013

    Will Quantum Gravity Get Us to the Stars?

    The Foundational Questions Institute (FQXi) 2nd International Conference in Ponta Delgada, Azores. July 7-12, 2009. Topics include cosmology, astrophysics, gravity, quantum gravity, quantum theory, and high-energy physics.

    The Meduso-Anthropic Principle is a speculative theory by Louis Crane (1994). The theory develops Cosmological natural selection by leading cosmologist, Lee Smolin and suggests the development of the universe is similar to the development of Corals and Jellyfish. The Medusa generations alternate with Polyp generations. Similarly it is suggested, the Universe develops Intelligent life and Intelligent life produces new Baby universes. Our universe may also exist as a Black hole in a Parallel universe. Extraterrestrial life there may have created that black hole.

    Bringing the Heavens down to Earth

    If mini black holes can be produced in high-energy particle interactions, they may first be observed in high-energy cosmic-ray neutrino interactions in the atmosphere. Jonathan Feng of the University of California at Irvine and MIT, and Alfred Shapere of the University of Kentucky have calculated that the Auger cosmic-ray observatory, which will combine a 6000 km2 extended air-shower array backed up by fluorescence detectors trained on the sky, could record tens to hundreds of showers from black holes before the LHC turns on in 2007......Thus, hypothetically, the energy required to produce black holes is well within the range of the LHC, making it a "black-hole factory". As Stephen Hawking has taught us, these mini black holes would be extremely hot little objects that would dissipate all their energy very rapidly by emitting radiation and particles before they wink out of existence. The properties of the Hawking radiation could tell us about the properties of the extra spatial dimensions, although there are still uncertainties in the theory at this stage. See: here
    We have been assured black hole production can be quite safe so we can deal with the idea  that such production quickly dissipates on the level with which we would and can make them?:)  So the level at which such an idea is presented would of course be as suggested as to say that this universe in all it's ability is at the level with which we can make black-holes useful?  Black holes of sufficient size.:) I find that really interesting,  just because we are here.

    See Also:

    Wednesday, August 07, 2013

    Lee Smolin: Cosmological Natural Selection

    Which leads to a prediction or an observation that after many, many generations the population of the universes should be fine-tuned to maximize the production of Black Holes. And that has further implications for things that we can actually try to measure and disprove experimentally. So that's, very briefly, the idea of cosmological natural selection.

    Tuesday, July 23, 2013

    Information Loss

    You see, people are uncomfortable with this information loss. It’s the minority view.Pg 64, The Cyclic Universe: A Conversation with Roger Penrose

    I am certainly uncomfortable with it, as I have always seen it from the idea  as to what is current in the field of discussion around blackholes and such. So there are things going on as I am reading the pdf discussion with Roger Penrose.  I am also listening to Susskind's lecture while correlating the perspective that is being talked about by Roger Penrose.

    I am adding this link just for some perspective about information and the presence of an anomaly that I perceive for such rules about past and future, and the topic of will. This as it relates too, the whole gamut of the science and investigation of what truly exists in terms of information.  Most surely,  I have some issues to deal with:)

    Tuesday, May 14, 2013

    Glowing Blackholes

    (Courtesy: NASA E/PO, Sonoma State University, Aurore Simonnet)
    The birth of a black hole may be signalled by a characteristic cosmic flash, according to researchers in the US. It was previously thought that only the most massive of black holes would produce gamma-ray bursts – narrow beams of electromagnetic radiation that shoot out of the poles of the collapsing star – when they form. But other dying stars were thought to produce a black hole without any kind of flash – seemingly disappearing from the visible sky in an event known as an "unnova". The US researchers' work suggests that unnovae might also have their own characteristic flash, allowing astronomers to witness the birth of stellar- and intermediate-mass black holes. See:
    Cosmic flashes could herald birth of black holes

    The continuing difficulty of achieving a reliable explosion in simulations of core-collapse supernovae, especially for more massive stars, has led to speculation concerning the observable transients that might be produced if such a supernova fails. Even if a prompt outgoing shock fails to form in a collapsing presupernova star, one must still consider the hydrodynamic response of the star to the abrupt loss of mass via neutrinos as the core forms a protoneutron star. Following a suggestion by Nadezhin (1980), we calculate the hydrodynamical responses of typical supernova progenitor stars to the rapid loss of approximately 0.2 to 0.5 M_sun of gravitational mass from their centers. In a red supergiant star, a very weak supernova with total kinetic energy ~ 10^47 erg results. The binding energy of a large fraction of the hydrogen envelope before the explosion is of the same order and, depending upon assumptions regarding the neutrino loss rates, most of it is ejected. Ejection speeds are ~ 100 km/s and luminosities ~ 10^39 erg/s are maintained for about a year. A significant part of the energy comes from the recombination of hydrogen. The color of the explosion is extremely red and the events bear some similarity to "luminous red novae," but have much lower speeds. See: Very Low Energy Supernovae from Neutrino Mass Loss

    See Also:

    Sunday, May 05, 2013

    The Blackhole Hunt is On

    Published on May 30, 2012

     See: NuSTAR to Hunt for Black Holes


    NASA contracted with Orbital Sciences Corporation to launch NuSTAR (mass 772 pounds (350 kg))[11] on a Pegasus XL rocket for 21 March 2012.[5] It had earlier been planned for 15 August 2011, 3 February 2012, 16 March 2012, and 14 March 2012.[12] After a launch meeting on 15 March 2012, the launch was pushed further back to allow time to review flight software used by the launch vehicle's flight computer.[13] The launch was conducted successfully at 16:00:37 UTC on 13 June 2012[1] about 117 nautical miles south of Kwajalein Atoll.[14] The Pegasus rocket was dropped from the L-1011 'Stargazer' aircraft.[11][15]
    On 22 June 2012 it was confirmed that the 10 m mast was fully deployed.[16]

    See Also:

    Sunday, September 23, 2012

    Black Hole Thoughts are Spoken: Complementarity vs Firewall

    Black Holes: Complementarity vs Firewalls

    • Subtitle: Strings 2012
    • Speaker: Raphael Bousso
    • Location: Ludwig-Maximilians-Universität München
    • Date: 27.07.2012 @ 16:04

    Ahmed Almheiri, Donald Marolf, Joseph Polchinski, James Sully

    We argue that the following three statements cannot all be true: (i) Hawking radiation is in a pure state, (ii) the information carried by the radiation is emitted from the region near the horizon, with low energy effective field theory valid beyond some microscopic distance from the horizon, and (iii) the infalling observer encounters nothing unusual at the horizon. Perhaps the most conservative resolution is that the infalling observer burns up at the horizon. Alternatives would seem to require novel dynamics that nevertheless cause notable violations of semiclassical physics at macroscopic distances from the horizon. Black Hole: Complementarity vs Firewall

    This lecture presents some particular thoughts that rang a bell for me in terms of what reporting was done here earlier on the thought experiments by Susskind on how one may interpret information gained by the process of entanglement to an observer outside the black hole.

    See:The elephant and the event horizon 26 October 2006 by Amanda Gefter at New Scientist.

     Also See: Where Susskind leaves off, Seth Lloyd begins

    Various neutron interferometry experiments demonstrate the subtlety of the notions of duality and complementarity. By passing through the interferometer, the neutron appears to act as a wave. Yet upon passage, the neutron is subject to gravitation. As the neutron interferometer is rotated through Earth's gravitational field a phase change between the two arms of the interferometer can be observed, accompanied by a change in the constructive and destructive interference of the neutron waves on exit from the interferometer. Some interpretations claim that understanding the interference effect requires one to concede that a single neutron takes both paths through the interferometer at the same time; a single neutron would "be in two places at once", as it were. Since the two paths through a neutron interferometer can be as far as 5 cm to 15 cm apart, the effect is hardly microscopic. This is similar to traditional double-slit and mirror interferometer experiments where the slits (or mirrors) can be arbitrarily far apart. So, in interference and diffraction experiments, neutrons behave the same way as photons (or electrons) of corresponding wavelength. See: Complementarity (physics)

    See Also:

    Tuesday, May 15, 2012

    Illusions of Grandeur?

    Illusions of Gravity

    Three spatial dimensions are visible all around us--up/down, left/right, forward/backward. Add time to the mix, and the result is a four-dimensional blending of space and time known as spacetime. Thus, we live in a four-dimensional universe. Or do we?

    Amazingly, some new theories of physics predict that one of the three dimensions of space could be a kind of an illusion--that in actuality all the particles and fields that make up reality are moving about in a two-dimensional realm like the Flatland of Edwin A. Abbott. Gravity, too, would be part of the illusion: a force that is not present in the two-dimensional world but that materializes along with the emergence of the illusory third dimension.

    UC Berkeley's Raphael Bousso presents a friendly introduction to the ideas behind the holographic principle, which may be very important in the hunt for a theory of quantum gravity. Series: "Lawrence Berkeley National Laboratory Summer Lecture Series" [3/2006] [Science] [Show ID: 11140]

    This is just a recoup of what had been transpiring since 2005. We have a pretty good picture of the ways such distinctions are held for perspective so that we may look inside the black hole? The labels of this blog entry help with this refreshing.

    See Also:

    Wednesday, March 26, 2008

    Blackhole Information Paradox

    What good is a universe without somebody around to look at it?
    Robert Dicke

    John Archibald Wheeler (born July 9, 1911) is an eminent American theoretical physicist. One of the later collaborators of Albert Einstein, he tried to achieve Einstein's vision of a unified field theory. He is also known as the coiner of the popular name of the well known space phenomenon, the black hole.

    There is always somebody who is the teacher and from them, their is a progeny. It would not be right not to mention John Archibald Wheeler. Or not to mention some of his students.

    Notable students
    Demetrios Christodoulou
    Richard Feynman
    Jacob Bekenstein
    Robert Geroch
    Bei-Lok Hu
    John R. Klauder
    Charles Misner
    Milton Plesset
    Kip Thorne
    Arthur Wightman
    Hugh Everett
    Bill Unruh

    COSMIC SEARCH: How did you come up with the name "black hole"?

    John Archibald Wheeler:It was an act of desperation, to force people to believe in it. It was in 1968, at the time of the discussion of whether pulsars were related to neutron stars or to these completely collapsed objects. I wanted a way of emphasizing that these objects were real. Thus, the name "black hole".

    The Russians used the term frozen star—their point of attention was how it looked from the outside, where the material moves much more slowly until it comes to a horizon.* (*Or critical distance. From inside this distance there is no escape.) But, from the point of view of someone who's on the material itself, falling in, there's nothing special about the horizon. He keeps on going in. There's nothing frozen about what happens to him. So, I felt that that aspect of it needed more emphasis.

    It is important to me to understand some of the history of the Blackhole, and the students who went on to develop the very ideas around them. To see how they interconnect at one time or another, to provide for the very insights from such gatherings.

    Stephen Hawking’s says:

    “Roger Penrose and I worked together on the large scale structure of space and time, including singularities and black holes. We pretty much agree on the classical theory of theory of relativity but disagreements began to emerge when we got into quantum gravity. We now have different approaches to the world, physical and mental. Basically, he is a Platonist believing that’s there’s a unique world of ideas that describes a unique physical reality. I on the other hand, am a positivist who believes that physical theories are just mathematical models we construct, and it is meaningless to ask if they correspond to reality; just whether they predict observations.”
    ( Chapter Six-The Large, the Small and the Human Mind-Roger Penrose-Cambridge University Press-1997)
    See: Phil Warnell's comment.

    Black hole information paradox

    Whereas Stephen Hawking and Kip Thorne firmly believe that information swallowed by a black hole is forever hidden from the outside universe, and can never be revealed even as the black hole evaporates and completely disappears,

    And whereas John Preskill firmly believes that a mechanism for the information to be released by the evaporating black hole must and will be found in the correct theory of quantum gravity,

    Therefore Preskill offers, and Hawking/Thorne accept, a wager that:

    When an initial pure quantum state undergoes gravitational collapse to form a black hole, the final state at the end of black hole evaporation will always be a pure quantum state.

    The loser(s) will reward the winner(s) with an encyclopedia of the winner's choice, from which information can be recovered at will.

    Stephen W. Hawking, Kip S. Thorne, John P. Preskill
    Pasadena, California, 6 February 1997

    Drawing Credit: XMM-Newton, ESA, NASA-Image sourced from: Pictured above is an artist's illustration of a black hole surrounded by an accretion disk.

    The black hole Information Paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could "disappear" in a black hole. It is a contentious subject since it violates a commonly assumed tenet of science—that information cannot be destroyed. If it is true, then cause and effect become unrelated, and nothing science knows, not even our memories, can be trusted.

    Before the Big Bang

    Professor Sir Roger Penrose, OM, FRS (born 8 August 1931) Before the Big Bang

    Three Different Views of Quantum Weirdness
    (and What It Means)

    A: According to the orthodox view of quantum mechanics, called the Copenhagen interpretation, a system (represented here by a child’s block) does not occupy a definite state or location until it is measured. Before then it is just a blur of overlapping possibilities.

    B: The many worlds interpretation insists that the system occupies all its possible states but that every one of them exists in its own alternate universe. Each universe sees one state only, which is why we never observe the block in two states at once.

    C: In Penrose’s interpretation, gravity holds our reality together. In each potential state, the block generates a separate gravitational field. Over time, the energy required to maintain these multiple fields causes the block to settle into one state only—the one that we observe.

    See:If an Electron Can Be in Two Places at Once, Why Can't You-by Tim Folger, Photograph by David Berry, Illustrations by Don Foley?

    "In Penrose’s interpretation, gravity holds our reality together. In each potential state, the block generates a separate gravitational field.....," rings with a certain importance when one talks about what happens with the very nature of the blackhole. What happens to that information.

    Phil Warnell:However, if the second is taken as truth and all is remembering, then what can the force of gravity do to a memory that is not in any, yet of all?

    I tried to implement a method by which one could "gauge the significance of the emotive experience" as it may pertain to that "primitive part" of our nature. That we could see "remembering" had been assigned a "quantum reductionist state" within the confines of that methodology?

    See:Quantum State reduction as a real phenomenon by Roger Penrose (Oxford)2 Sep 1999

    "The block," while holding different gravitational defined consciousness states, had to settle to a strong emotive consolidating force from that experience. You repeatedly relive the experience, while current information saids that the memory can change. See Ledoux.


    Dennis William Sciama
    Tipping LightCones and Escape Velocity of the Photon
    What is Happening at the Singularity?
    Science and the Mind: Sir Roger Penrose
    Big Bang:One Man's Change of Heart

    Saturday, March 08, 2008

    Stringy Geometry

    fancier way of saying that is that in general, it's okay to model the space around us using the Euclidean metric. But the Euclidean model stops working when gravity becomes strong, as we'll see later. The Euclidean model for space

    The magic square of "Albrect Durer" located in my index on the right is fascinating from the point of view that such a symmetry can be derived from the view of moving in an abstract space.

    Trying to understand the implication of what is happening in a stronger gravitational field is an abstract journey for me as well, while I hold "thoughts of lensing" in my mind as a accumulative effect of something that is happening naturally out in space.

    The move to Lagrangian points out in space is also an accumulative effect of thinking in this abstract way.

    I not only think of the "magnetic field as as an associative value for that abstractness," it is a geometry that is the same for me, as I try to unravel the energy valuation of points(KK Tower) of any location in space. While the valuation of a circle on a 2 dimensional screen sees a string vibrating, I am moving this perception to valuations onto mathematical models.

    I have nobody to help this way I have to push forward, knowing there will be mistakes, and that hopefully I am grasping the full scope of seeing in a abstract way.

    Figure 2. Clebsch's Diagonal Surface: Wonderful.
    We are told that "mathematics is that study which knows nothing of observation..." I think no statement could have been more opposite to the undoubted facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activity of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world, ...that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of imagination and invention. ...Were it not unbecoming to dilate on one's personal experience, I could tell a story of almost romantic interest about my own latest researches in a field where Geometry, Algebra, and the Theory of Numbers melt in a surprising manner into one another.

    Dr. Kip Thorne, Caltech 01-Relativity-The First 20th Century Revolution

    It was the beginning of what might be called (and in fact is called) Stringy Geometry. The point is that strings are not points, and specifically, their extended nature means that in addition to being able to see the usual geometrical properties of a space that the theory like General Relativity can see, the strings can see other, intrinsically stringy, data. There is a quantity in the theory that is called the Kalb-Ramond field (or just the “B-field”) that can be used to measure how much the string can winds on or wraps a piece of the geometry, in essence. The parameter a that measures the size of a piece of the space that collapses when the geometry becomes singular, is essentially joined by another parameter, b, that sort of measures how much the strings have wound or smeared themselves on that piece of the space. The upshot is that a and b naturally combine themselves into a complex parameter that naturally describes the resolution process, solving the puzzle that the Mathematicians faced.
    Beyond Einstein: Fixing Singularities in Spacetime

    I am always trying to get the "visual models" of such proposals in terms of the B Field. Nigel Hitchin

    Can you tell me, if the Dynkin diagrams and the points on a Sylvestor surface/ Cayley model have some value when looking at this subject?

    Also, if it would be wrong to see "UV coordinates of a Gaussian arc" can be seen in this light as well?

    I am recording this to help me understand how energy windings of the string may be seen as points on the Sylvester Surface?

    See: What is Happening at the Singularity?

    Friday, March 07, 2008

    What is Happening at the Singularity?

    WEll, some of the commentors like myself are not worth counting?:)Thanks for keeping it interesting Clifford of Asymptotia. I hope you won't mind the following quotes for consideration.( it was considered spam) so I reprint it here.

    Quantum geometry differs in substantial ways from the classical geometry underlying general relativity. For instance, topology change (the "tearing" of space) is a sensible feature of quantum geometry even though, from a classical perspective, it involves singularities. As another example, two different classical spacetime geometries can give rise to identical physical implications, again at odds with conclusions based on classical general relativity. Brian Greene

    Is there not some way presented by Susskind which can help one approach understanding of what is going on in the blackhole by incorporating his "thought experiment" in relation to the entanglement process?

    So of course questions about "the horizon" are interesting.

    Consider any physical system, made of anything at all- let us call it, The Thing. We require only that The Thing can be enclosed within a finite boundary, which we shall call the Screen(Figure39). We would like to know as much as possible about The Thing. But we cannot touch it directly-we are restricted to making measurements of it on The Screen. We may send any kind of radiation we like through The Screen, and record what ever changes result The Screen. The Bekenstein bound says that there is a general limit to how many yes/no questions we can answer about The Thing by making observations through The Screen that surrounds it. The number must be less then one quarter the area of The Screen, in Planck units. What if we ask more questions? The principle tells us that either of two things must happen. Either the area of the screen will increase, as a result of doing an experiment that ask questions beyond the limit; or the experiments we do that go beyond the limit will erase or invalidate, the answers to some of the previous questions. At no time can we know more about The thing than the limit, imposed by the area of the Screen. Page 171 and 172 0f, Three Roads to Quantum Gravity, by Lee Smolin

    TWO UNIVERSES of different dimension and obeying disparate physical laws are rendered completely equivalent by the holographic principle. Theorists have demonstrated this principle mathematically for a specific type of five-dimensional spacetime ("anti–de Sitter") and its four-dimensional boundary. In effect, the 5-D universe is recorded like a hologram on the 4-D surface at its periphery. Superstring theory rules in the 5-D spacetime, but a so-called conformal field theory of point particles operates on the 4-D hologram. A black hole in the 5-D spacetime is equivalent to hot radiation on the hologram--for example, the hole and the radiation have the same entropy even though the physical origin of the entropy is completely different for each case. Although these two descriptions of the universe seem utterly unalike, no experiment could distinguish between them, even in principle. by Jacob D. Bekenstein

    The old version of string theory, pre-1995, had these first two features. It includes quantum mechanics and gravity, but the kinds of things we could calculate were pretty limited. All of a sudden in 1995, we learned how to calculate things when the interactions are strong. Suddenly we understood a lot about the theory. And so figuring out how to compute the entropy of black holes became a really obvious challenge. I, for one, felt it was incumbent upon the theory to give us a solution to the problem of computing the entropy, or it wasn't the right theory. Of course we were all gratified that it did. Black Holes and Beyond: Harvard's Andrew Strominger on String Theory

    So we have these diagrams and thought processes developed from individuals like Jacob D. Bekenstein to help us visualize what is taking place. Gives us key indicators of the valuation needed, in order to determine what maths are going to be used? In this case the subject of Conformal Field Theory makes itself known, for the thought process?

    Holography encodes the information in a region of space onto a surface one dimension lower. It sees to be the property of gravity, as is shown by the fact that the area of th event horizon measures the number of internal states of a blackhole, holography would be a one-to-one correspondence between states in our four dimensional world and states in higher dimensions. From a positivist viewpoint, one cannot distinguish which description is more fundamental.Pg 198, The Universe in Nutshell, by Stephen Hawking

    So we are given the label in which to speak about the holographic notions of what is being talked about in the case of the blackhole's horizon.

    Campbell's Soup Can by Andy Warhol Exhibited in New York (USA), Leo Castelli Gallery

    Spacetime in String Theory-Dr. Gary Horowitz, UCSB-Apr 20, 2005

    This year marks the hundredth anniversary of Einstein's "miraculous year", 1905, when he formulated special relativity, and explained the origin of the black body spectrum and Brownian motion. In honor of this occasion, I will describe the modern view of spacetime. After reviewing the properties of spacetime in general relativity, I will provide an overview of the nature of spacetime emerging from string theory. This is radically different from relativity. At a perturbative level, the spacetime metric appears as ``coupling constants" in a two-dimensional quantum field theory. Nonperturbatively (with certain boundary conditions), spacetime is not fundamental but must be reconstructed from a holographic, dual theory. I will conclude with some recent ideas about the big bang arising from string theory.

    The purpose of this note is to provide a possible answer to this question. Rather than the radical modification of quantum mechanics required for pure states to evolve into mixed states, we adopt a more mild modification. We propose that at the black hole singularity one needs to impose a unique final state boundary condition. More precisely, we have a unique final wavefunction for the interior of the black hole. Modifications of quantum mechanics where one imposes final state boundary conditions were considered in [6,7,8,9]. Here we are putting a final state boundary condition on part of the system, the interior of the black hole. This final boundary condition makes sure that no information is “absorbed” by the singularity.Gary T. Horowitz and Juan Maldacena,

    See: Stringy Geometry