White hole

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For other uses, see White hole (disambiguation).

A white hole, in general relativity, is a hypothetical region of spacetime which cannot be entered from the outside, but from which matter and light may escape. In this sense it is the reverse of a black hole, which can be entered from the outside, but from which nothing, including light, may escape. (However, it is theoretically possible for a traveler to enter a rotating black hole, avoid the singularity, and travel into a rotating white hole which allows the traveler to escape into another universe.[1]) White holes appear in the theory of eternal black holes. In addition to a black hole region in the future, such a solution of the Einstein equations has a white hole region in its past.[2] However, this region does not exist for black holes that have formed through gravitational collapse, nor are there any known physical processes through which a white hole could be formed.

Like black holes, white holes have properties like mass, charge, and angular momentum. They attract matter like any other mass, but objects falling towards a white hole would never actually reach the white hole's event horizon (though in the case of the maximally extended Schwarzschild solution, discussed below, the white hole event horizon in the past becomes a black hole event horizon in the future, so any object falling towards it will eventually reach the black hole horizon).

In quantum mechanics, the black hole emits Hawking radiation, and so can come to thermal equilibrium with a gas of radiation. Since a thermal equilibrium state is time reversal invariant, Stephen Hawking argued that the time reverse of a black hole in thermal equilibrium is again a black hole in thermal equilibrium.[3] This implies that black holes and white holes are the same object. The Hawking radiation from an ordinary black hole is then identified with the white hole emission. Hawking's semi-classical argument is reproduced in a quantum mechanical AdS/CFT treatment,[4] where a black hole in anti-de Sitter space is described by a thermal gas in a gauge theory, whose time reversal is the same as itself.

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[edit] Origin

White holes appear as part of a solution to the Einstein field equations known as the maximally extended version of the Schwarzschild metric describing an eternal black hole with no charge and no rotation. Here, "maximally extended" refers to the idea that the spacetime should not have any "edges": for any possible trajectory of a free-falling particle (following a geodesic) in the spacetime, it should be possible to continue this path arbitrarily far into the particle's future, unless the trajectory hits a gravitational singularity like the one at the center of the black hole's interior. In order to satisfy this requirement, it turns out that in addition to the black hole interior region which particles enter when they fall through the event horizon from the outside, there must be a separate white hole interior region which allows us to extrapolate the trajectories of particles which an outside observer sees rising up away from the event horizon. For an observer outside using Schwarzschild coordinates, infalling particles take an infinite time to reach the black hole horizon infinitely far in the future, while outgoing particles which pass the observer have been traveling outward for an infinite time since crossing the white hole horizon infinitely far in the past (however, the particles or other objects experience only a finite proper time between crossing the horizon and passing the outside observer). The black hole/white hole appears "eternal" from the perspective of an outside observer, in the sense that particles traveling outward from the white hole interior region can pass the observer at any time, and particles traveling inward which will eventually reach the black hole interior region can also pass the observer at any time.

Just as there are two separate interior regions of the maximally extended spacetime, there are also two separate exterior regions, sometimes called two different "universes", with the second universe allowing us to extrapolate some possible particle trajectories in the two interior regions. This means that the interior black-hole region can contain a mix of particles that fell in from either universe (and thus an observer who fell in from one universe might be able to see light that fell in from the other one), and likewise particles from the interior white-hole region can escape into either universe. All four regions can be seen in a spacetime diagram which uses Kruskal–Szekeres coordinates, as discussed and illustrated on the page White Holes and Wormholes.

In this spacetime, it is possible to come up with coordinate systems such that if you pick a hypersurface of constant time (a set of points that all have the same time coordinate, such that every point on the surface has a space-like separation, giving what is called a 'space-like surface') and draw an "embedding diagram" depicting the curvature of space at that time (see the discussion of embedding diagrams on this page), the embedding diagram will look like a tube connecting the two exterior regions, known as an "Einstein-Rosen bridge" or Schwarzschild wormhole. For example, see the diagrams on this page which show the maximally extended Schwarzschild solution in Kruskal–Szekeres coordinates along with white hypersurfaces of constant time drawn on(time in some other coordinate system besides Kruskal–Szekeres coordinates, since a hypersurface of constant Kruskal–Szekeres time would just look like a horizontal line when drawn in a Kruskal–Szekeres diagram), and the corresponding embedding diagram for that hypersurface. Depending on where the space-like hypersurface is chosen, the Einstein-Rosen bridge can either connect two black hole event horizons in each universe (with points in the interior of the bridge being part of the black hole region of the spacetime), or two white hole event horizons in each universe (with points in the interior of the bridge being part of the white hole region). It is impossible to use the bridge to cross from one universe to the other, however, because it is impossible to enter a white hole event horizon from the outside, and anyone entering a black hole horizon from either universe will inevitably hit the black hole singularity.

Note that the maximally extended Schwarzschild metric describes an idealized black hole/white hole that exists eternally from the perspective of external observers; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric. When the infalling stellar matter is added to a diagram of a black hole's history, it removes the part of the diagram corresponding to the white hole interior region.[5] But because the equations of general relativity are time-reversible (they exhibit T-symmetry), general relativity must also allow the time-reverse of this type of "realistic" black hole that forms from collapsing matter. The time-reversed case would be a white hole that has existed since the beginning of the universe, and which emits matter until it finally "explodes" and disappears.[6] Despite the fact that such objects are permitted theoretically, they are not taken as seriously as black holes by physicists, since there would be no processes that would naturally lead to their formation, they could only exist if they were built into the initial conditions of the Big Bang.[6] Additionally, it is predicted that such a white hole would be highly "unstable" in the sense that if any small amount of matter fell towards the horizon from the outside, this would prevent the white hole's explosion as seen by distant observers, with the matter emitted from the singularity never able to escape the white hole's gravitational radius.[7]

[edit] Recent speculations

There are theories suggesting that white holes create new universes from matter originating in another universe's black hole.[8]

A more recently proposed view of black holes might be interpreted as shedding some light on the nature of classical white holes. Some researchers have proposed that when a black hole forms, a big bang occurs at the core, which creates a new universe that expands outside of the parent universe.[9][10] See also Fecund universes.

The initial feeding of matter from the parent universe's black hole and the expansion that follows in the new universe might be thought of as a cosmological type of white hole. Unlike traditional white holes, this type of white hole would not be localized in space in the new universe, and its horizon would have to be identified with the cosmological horizon.[citation needed]

However, the second law of thermodynamics states that "in all energy exchanges, if no energy enters or leaves the system, the potential energy of the state will always be less than that of the initial state." White holes apparently do not follow this law, and there is much speculation on the issue of whether or not white holes exist.

If you enter a black hole then you would come out of the corresponding white hole in the same condition that you entered the black hole. When you exit the white hole it will be in the past, the time that you leave will depend on the distance the white hole is from the black hole.

[edit] See also

[edit] References

  1. ^ See the bottom diagram at http://jila.colorado.edu/~ajsh/insidebh/penrose.html for an illustration using a Penrose diagram
  2. ^ Carroll, Sean M. (2004). Spacetime and Geometry (5.7 ed.). Addison Wesley. ISBN 0-8053-8732-3. 
  3. ^ Hawking, S. W. (1976). "Black Holes and Thermodynamics". Physical Review D 13 (2): 191–197. Bibcode 1976PhRvD..13..191H. doi:10.1103/PhysRevD.13.191. 
  4. ^ Klebanov, Igor R. (19 May 2006). TASI lectures: Introduction to the AdS/CFT correspondence. arXiv:hep-th/0009139v2. Bibcode 2001sbg..conf..615K. doi:10.1142/9789812799630_0007. hep-th/0009139 v2. 
  5. ^ http://casa.colorado.edu/~ajsh/collapse.html#kruskal
  6. ^ a b Wheeler, J. Craig (2007). Cosmic Catastrophes: Exploding Stars, Black Holes, and Mapping the Universe. Cambridge University Press. pp. 197–198. ISBN 978-0521857147. 
  7. ^ Frolov, Valeri P.; Igor D. Novikov (1998). Black Hole Physics: Basic Concepts and New Developments. Springer. pp. 580–581. ISBN 978-0792351450. 
  8. ^ http://news.nationalgeographic.com/news/2010/04/100409-black-holes-alternate-universe-multiverse-einstein-wormholes/
  9. ^ E. Fahri and A. H. Guth (1987). "An Obstacle to Creating a Universe in the Laboratory". Physics Letters B183 (2): 149. Bibcode 1987PhLB..183..149F. doi:10.1016/0370-2693(87)90429-1. 
  10. ^ Nikodem J. Poplawski (2010). "Radial motion into an Einstein–Rosen bridge". Physics Letters B 687 (2-3): 110–113. Bibcode 2010PhLB..687..110P. doi:10.1016/j.physletb.2010.03.029. http://newsinfo.iu.edu/news/page/normal/13995.html. 

[edit] External links

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