Naked singularity

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In the general theory of relativity (GTR), a naked singularity is a gravitational singularity , i.e. a hypothetical point in space-time with infinite curvature , but which, unlike a black hole, is not surrounded by an event horizon . The existence of such singularities would mean that it would be possible to observe a perfect gravitational collapse from the outside, even in areas in which the solutions are no longer mathematically defined according to the classical GTR equations.

Stephen Hawking and Roger Penrose had shown at the end of the 1960s under very general conditions that in general relativity singularities are to be expected and these cannot be avoided ( singularity theorem ).

Bulk

The question of whether naked singularities also occur in nature is answered in the negative by Roger Penrose , among others, in the assumption of a noumenon , which he calls a cosmic censorship. Penrose's cosmic censorship hypothesis has been supported by many astrophysicists, such as John Archibald Wheeler and Stephen Hawking . Others, like Kip Thorne , considered the possibility of the formation of naked singularities to be possible, for example in the case of strongly non-spherical collapse. In the early 1970s Thorne studied the (unphysical) case of the gravitational collapse of an infinitely longitudinally extended non-rotating thin cylinder and found that no event horizons were formed. Computer simulations of the gravitational collapse of mass distributions in the form of an elongated spheroid by Stuart L. Shapiro and Saul Teukolsky also indicated the possibility of bare singularities (although the simulations cannot prove that, they just showed that no apparent horizon was forming). In 1972 Thorne formulated the ring criterion as a limit to the extent of anisotropy in the event of a collapse, in which black holes are still formed and no naked singularities (hoop conjecture).

The cosmic censorship hypothesis can also be formulated more precisely mathematically.

Hawking, Thorne and Preskill bet and provisional resolution based on the results of mathematicians

In 1991, Hawking entered into a bet with Thorne and John Preskill as to whether naked singularities could appear in the GTR. Quantum effects were excluded. Hawking, who took the position that there are no naked singularities in GTR, admitted even a few months after placing the bet that naked singularities could possibly be left behind when black holes were evaporated, but did not see this as relevant for the bet because it did Quantum effects and not the emergence within the classic ART concerned. After Matthew Choptuik showed the possibility of naked singularities with scalar matter in 1993 (but for "non-generic" initial conditions) Hawking admitted the loss of the bet, but it was renewed in 1997 with restriction to generic initial conditions. Around the same time as Choptuik, Demetrios Christodoulou showed mathematically that naked singularities can form in gravitational collapse with scalar fields within the framework of general relativity (1992, published 1994), but shortly afterwards he also showed that these are unstable.

Rotating black holes and thought experiments

In the case of the rotating black holes described by the Kerr metric , with a sufficiently high rotation ( with the Kerr parameter , which is proportional to the angular momentum ), the event horizon would “tear open” and thus the cosmic censorship would be violated. More recent computer simulations from 2009 suggest that black holes would retain their event horizon even in the event of an ultra-relativistic collision with another black hole and that the limit would not be reached, even if one came very close to it. Thorne himself saw in 1994 a work by Werner Israel on the third law of the dynamics of black holes ensured that the limit value is unattainable. Analogous to the third law of thermodynamics , this states that the surface gravity of the black hole, which corresponds to the Hawking temperature , cannot be reduced to zero by any physical process (the disappearance would correspond to the Kerr solution ).

Arguments supporting the cosmic censorship hypothesis are the stability of the Schwarzschild solution and Kerr solution against small linear perturbations and thought experiments with extreme black holes. For charged, rotating black holes ( Kerr-Newman metric ) these are defined by ( as above). If the right side becomes larger than the left, there are no black holes as stationary solutions of the associated equations, which would presumably result in naked singularities. It is not possible to transfer charge or angular momentum to the extreme black hole with small test particles, as Robert Wald showed in 1974 and as various new analyzes of such thought experiments have shown. However, if one does not assume an extreme black hole (in the Reissner-Nordström solution), but one that comes as close as desired, Veronika Hubeny found a way to overcome the barrier with a charged test particle in 1998. This showed that this simple test model for Cosmic Censorship was not yet fully understood.

Observations

There is no astronomical evidence for the existence of naked singularities. For George FR Ellis , however, they are part of his alternative physical worldview, and according to the standard model of cosmology , the big bang can be understood as a naked singularity. Here and also when considering other naked singularities, questions of quantum gravity would play a role that go beyond the GTR.

Astrophysicists proposed a distinction between ordinary black holes and rapidly rotating naked singularities by their gravitational lensing effect. Other suggestions concerned the precession behavior of incident matter in the strongly distorted spacetime in the vicinity of the compact objects or the redshift of photons passing through the edge.

Strong cosmic censorship hypothesis

In addition to the weak cosmic censorship hypothesis discussed above, that the singularities of the GTR are enclosed by event horizons, there is also a strong cosmic censorship hypothesis. It generally excludes time-like singularities: even an observer who falls into the black hole will, according to the hypothesis, never “see” the singularity.

Cosmic Censorship in higher dimensions and other spacetime geometries, in connection with Weak Gravity Conjecture

In 2010, Frans Pretorius and Luis Lehner found a mechanism (black strings) to generate naked singularities in five or more dimensions.

In 2017, Toby Crisford and Jorge Santos were able to link the cosmic censorship hypothesis by simulating the Einstein-Maxwell equations in four-dimensional anti-de-sitter space (i.e. a different spacetime geometry than in our universe) with another hypothesis, namely the that gravity is always the weakest of the fundamental interactions (Weak gravity conjecture by Cumrun Vafa , Nima Arkani-Hamed , Lubos Motl, Alberto Nicolis, 2006). They found a counterexample to the weak cosmic censorship hypothesis, which is valid again if the gravitation relative to the other interactions (in this model case, electromagnetism) is set so that it is weakest. According to Nima Arkani-Hamed and Gary Horowitz , for example, this would also be an argument for a theory of quantum gravity, in which gravity is treated on the same level as the other interactions as in string theory, unlike in loop quantum gravity.

Others

Tsvi Piran and Amos Ori showed in 1990 that naked singularities are generically modeled in the gravitational collapse of matter as perfect, barotropic liquid.

Web links

Individual evidence

  1. ^ First in 1969 in Penrose: Gravitational collapse: the role of general relativity . In: Rivista del Nuovo Cimento , Numero Special, 1, 1969, p. 252
  2. ↑ Reinhard Breuer : Astrophysics: The case of the cosmic censor . In: Die Zeit , No. 38/1983
  3. ↑ a b Thorne: Black Holes and Time Warps . Norton, 1994, p. 481
  4. ↑ Thorne: Non spherical gravitational collapse, a short review . In: Klauder (Ed.): Magic without magic . Freeman, 1972, pp. 231-258
  5. ^ Shapiro, Teukolsky: Black holes, naked singularities and cosmic censorship . In: American Scientist , Volume 79, 1991, pp. 330-343
  6. ↑ E.g. R. Wald: Gravitational collapse and cosmic censorship . 1997, arxiv : gr-qc / 9710068 Chapter 2
  7. ↑ Thorne: Black Holes and Time Warps . Norton, 1994, p. 482
  8. ↑ Choptuik: Universality and scaling in gravitational collapse of a massless scalar field . In: Phys. Rev. Lett. , Volume 70, 1993, p. 9
  9. ↑ In any small neighborhood, solutions were found that were shielded by event horizons or did not lead to any singularity at all. See also Gary Horowitz: Creating naked singularities and negative energy . In: Physica Scripta , Volume T 117, 2005, pp. 86-91, arxiv : hep-th / 0312123
  10. ↑ Stephen Hawking, John Preskill, Kip Thorne: New bet on naked singularities. February 5, 1997, accessed February 21, 2017 (mentions the older losing bet).
  11. ↑ Demetrios Christodoulou : Examples of Naked Singularity Formation in Gravitational Collapse of a Scalar Field . In: Annals of Mathematics . 104, 1994, pp. 607-665
  12. ^ Demetrios Christodoulou : The Instability of Naked Singularities in the Gravitational Collapse of a Scalar Field. In: Annals of Mathematics . 149, 1999, pp. 183-217
  13. ↑ Ulf von Rauchhaupt : Naked singles are unfortunately not very stable. In: Frankfurter Allgemeine Sonntagszeitung . May 5, 2013, accessed February 21, 2017 .
  14. ↑ No naked black holes - Even high-speed mergers keep an event horizon . (PDF; 93 kB) ScienceNews, October 2008
  15. ↑ U. Sperhake, V. Cardoso, F. Pretorius, E. Berti, T. Hinderer, N. Yunes: Cross section, final spin and zoom-whirl behavior in high-energy black hole collisions . In: Phys. Rev. Lett. , Volume 103, 2009, p. 131102, Arxiv
  16. ^ W. Israel: Third law of black hole dynamics - a formulation and proof . In: Phys. Rev. Lett. , Volume 57, 1986, p. 397
  17. ↑ Thorne: Black Holes and Time Warps . Norton, 1994, p. 293
  18. ↑ The matter near the event horizon must meet the weak energy condition.
  19. ↑ Forest: Thought experiments to destroy a black hole . In: Annals of Physics , Volume 82, 1974, p. 548.
  20. ^ R. Wald: Gravitational collapse and cosmic censorship . 1997, arxiv : gr-qc / 9710068
  21. ↑ Hubeny: Overcharging a Black Hole and Cosmic Censorship . In: Phys. Rev. D , Volume 59, 1999, p. 064013, arxiv : gr-qc / 9808043
  22. ↑ Steven Battersby: Is a 'naked singularity' lurking in our galaxy? New Scientist, October 1, 2007
  23. ↑ Chakraborty u. a .: Spin precession in a black hole and naked singularity spacetimes . In: Phys. Rev. D , Volume 95, 2017, p. 044006, arxiv : 1605.00600
  24. ^ Néstor Ortiz, Olivier Sarbach, Thomas Zannias: Observational distinction between black holes and naked singularities: the role of the redshift function . In: Classical and Quantum Gravity , Volume 32, 2015, p. 247001, arxiv : 1401.4227
  25. ^ Penrose in: Hawking, Israel: General Relativity, an Einstein centenary survey . Cambridge UP, 1979
  26. ^ Lehner, Pretorius: Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship . In: Phys. Rev. Lett. , Volume 105, 2010, p. 101102, arxiv : 1006.5960
  27. ↑ Crisford, Santos: Violating weak cosmic censorship in ADS4 . In: Phys. Rev. Lett. , Volume 118, 2017, p. 181101, arxiv : 1702.05490
  28. ↑ Crisford Santos, Gary Horowitz : Testing the Weak Gravity - Cosmic Censorship Connection . In: Phys. Rev. D , Volume 97, 2018, p. 066005, arxiv : 1709.07880
  29. ^ Nima Arkani-Hamed, Lubos Motl, Alberto Nicolis, Cumrun Vafa: The String Landscape, Black Holes and Gravity as the Weakest Force . In: JHEP , 0706, 2007, p. 060, arxiv : hep-th / 0601001
  30. ↑ Natalie Wolchover: Where Gravity Is Weak and Naked Singularities Are Verboten . In: Quanta Magazine , July 20, 2017
  31. ↑ Amos Ori, Tsvi Piran: Naked singularities and other features of self-similar general-relativistic gravitational collapse, Physical Review D, Volume 42, 1990, pp. 1068-1090. Abstract