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No-hair theorem

no hair theorem, black hole 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 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" which was the origin of the name In a later interview, John Wheeler says that Jacob Bekenstein coined this phrase

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 The result was quickly generalized to the cases of charged or spinning black holes 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 ie, 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

Contents

  • 1 Example
  • 2 Changing the reference frame
  • 3 Extensions
  • 4 Counterexamples
  • 5 Observational results
  • 6 See also
  • 7 References
  • 8 External links

Example

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 ie, the global charges baryonic number, leptonic number, etc are conserved in the black hole

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:

  • mass-energy M,
  • linear momentum P three components,
  • angular momentum J three components,
  • position X three components,
  • electric charge Q

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: mass, angular momentum magnitude, and electric charge 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

Extensions

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, etc

It has since been extended to include the case where the cosmological constant is positive which recent observations are tending to support

Magnetic charge, if detected as predicted by some theories, would form the fourth parameter possessed by a classical black hole

Counterexamples

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" 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 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 some experimental evidence consistent with the uniqueness or no-hair theorem This observation is consistent with Stephen Hawking's theoretical work on black holes in the 1970s

See also

  • Black hole information paradox
  • Event Horizon Telescope

References

  1. ^ a b 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 
  2. ^ "Interview with John Wheeler 2/3" – via YouTube 
  3. ^ Israel, Werner 1967 "Event Horizons in Static Vacuum Space-Times" Phys Rev 164 5: 1776–1779 Bibcode:1967PhRv1641776I doi:101103/PhysRev1641776 
  4. ^ Israel, Werner 1968 "Event horizons in static electrovac space-times" Commun Math Phys 8 3: 245–260 Bibcode:1968CMaPh8245I doi:101007/BF01645859 
  5. ^ Carter, Brandon 1971 "Axisymmetric Black Hole Has Only Two Degrees of Freedom" Phys Rev Lett 26 6: 331–333 Bibcode:1971PhRvL26331C doi:101103/PhysRevLett26331 
  6. ^ Bhattacharya, Sourav; Lahiri, Amitabha 2007 "No hair theorems for positive Λ" Physical Review Letters 99 20 arXiv:gr-qc/0702006v2  Bibcode:2007PhRvL99t1101B doi:101103/PhysRevLett99201101 
  7. ^ Mavromatos, N E 1996 "Eluding the No-Hair Conjecture for Black Holes" arXiv:gr-qc/9606008v1  
  8. ^ 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:2005PhRvL94l1101Z doi:101103/PhysRevLett94121101 PMID 15903901 
  9. ^ "Gravitational waves from black holes detected" BBC News 11 February 2016 
  10. ^ https://physicsapsorg/articles/v9/52
  11. ^ https://wwwfacebookcom/stephenhawking/posts/965377523549345 Stephen Hawking
  12. ^ https://wwwbbccom/news/science-environment-35551144 Stephen Hawking celebrates gravitational wave discovery

External links

  • Hawking, S W 2005 "Information Loss in Black Holes" Physical Review D 72 8 arXiv:hep-th/0507171v2  Bibcode:2005PhRvD72h4013H doi:101103/PhysRevD72084013 , Stephen Hawking’s purported solution to the black hole unitarity paradox, first reported in July 2004

black hole no hair theorem, no hair theorem


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No-hair theorem


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    No-hair theorem beatiful post thanks!

    29.10.2014


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