Monday, July 18, 2016

Can black holes tunnel to white holes?

Tl;dr: Yes, but it’s unlikely.

If black holes attract your attention, white holes might blow your mind.

A white hole is a time-reversed black hole, an anti-collapse. While a black hole contains a region from which nothing can escape, a white hole contains a region to which nothing can fall in. Since the time-reversal of a solution of General Relativity is another solution, we know that white holes exist mathematically. But are they real?

Black holes were originally believed to merely be of mathematical interest, solutions that exist but cannot come into being in the natural world. As physicists understood more about General Relativity, however, the exact opposite turned out to be the case: It is hard to avoid black holes. They generically form from matter that collapses under its own gravitational pull. Today it is widely accepted that the black hole solutions of General Relativity describe to high accuracy astrophysical objects which we observe in the real universe.

The simplest black hole solutions in General Relativity are the Schwarzschild-solutions, or their generalizations to rotating and electrically charged black holes. These solutions however are not physically realistic because they are entirely time-independent, which means such black holes must have existed forever. Schwarzschild black holes, since they are time-reversal invariant, also necessarily come together with a white hole. Realistic black holes, on the contrary, which are formed from collapsing matter, do not have to be paired with white holes.

(Aside: Karl Schwarzschild was German. Schwarz means black, Schild means shield. Probably a family crest. It’s got nothing to do with children.)

But there are many things we don’t understand about black holes, most prominently how they handle information of the matter that falls in. Solving the black hole information loss problem requires that information finds a way out of the black hole, and this could be done for example by flipping a black hole over to a white hole. In this case the collapse would not complete, and instead the black hole would burst, releasing all that it had previously swallowed.

It’s an intriguing and simple option. This black-to-white-hole transition has been discussed in the literature for some while, recently by Rovelli and Vidotto in the Planck star idea. It’s also subject of a last week’s paper by Barcelo and Carballo-Rubio.

Is this a plausible solution to the black hole information loss problem?

It is certainly possible to join part of the black hole solution with part of the white hole solution. But doing this brings some problems.

The first problem is that at the junction the matter must get a kick that transfers it from one state into the other. This kick cannot be achieved by any known physics – we know this from the singularity theorems. There isn’t anything in the known physics can prevent a black hole from collapsing entirely once the horizon is formed. Whatever makes this kick hence needs to violate one of the energy conditions, it must be new physics.

Something like this could happen in a region with quantum gravitational effects. But this region is normally confined to deep inside the black hole. A transition to a white hole could therefore happen, but only if the black hole is very small, for example because it has evaporated for a long time.

But this isn’t the only problem.

Before we think about the stability of black holes, let us think about a simpler question. Why doesn’t dough unmix into eggs and flour and sugar neatly separated? Because that would require an entropy decrease. The unmixing can happen, but it’s exceedingly unlikely, hence we never see it.

A black hole too has entropy. It has indeed enormous entropy. It saturates the possible entropy that can be contained within a closed surface. If matter collapses to a black hole, that’s a very likely process to happen. Consequently, if you time-reverse this collapse, you get an exceedingly unlikely process. This solution exists, but it’s not going to happen unless the black hole is extremely tiny, close by the Planck scale.

It is possible that the white hole which a black hole supposedly turns into is not the exact time-reverse, but instead another solution that further increases entropy. But in that case I don’t know where this solution comes from. And even so I would suspect that the kick required at the junction must be extremely finetuned. And either way, it’s not a problem I’ve seen addressed in the literature. (If anybody knows a reference, please let me know.)

In a paper written for the 2016 Awards for Essays on Gravitation, Haggard and Rovelli make an argument in favor of their idea, but instead they just highlight the problem with it. They claim that small quantum fluctuations around the semi-classical limit which is General Relativity can add up over time, eventually resulting in large deviations. Yes, this can happen. But the probability that this happens is tiny, otherwise the semi-classical limit wouldn’t be the semi-classical limit.

The most likely thing to happen instead is that quantum fluctuations average out to give back the semi-classical limit. Hence, no white-hole transition. For the black-to-white-hole transition one would need quantum fluctuations to conspire together in just the right way. That’s possible. But it’s exceedingly unlikely.

In the other recent paper the authors find a surprisingly large transition rate for black to white holes. But they use a highly symmetrized configuration with very few degrees of freedom. This must vastly overestimate the probability for transition. It’s an interesting mathematical example, but it has very little to do with real black holes out there.

In summary: That black holes transition to white holes and in this way release information is an idea appealing because of its simplicity. But I remain unconvinced because I am missing a good argument demonstrating that such a process is likely to happen.


  1. "their generalizations to rotating and electrically charged black holes"

    The Kerr and Kerr-Newman solutions. Roy Kerr is still alive at 82, Ted Newman at 86.

    One can see both in this excellent video, along with a who's who of the Golden Age of General Relativity. You can even see my balding head in the audience. :-) Ted Newman got the most laughs for a story about hiking. Bonus points if you can spot the link from this story to me.

  2. "(Aside: Karl Schwarzschild was German. Schwarz means black, Schild means shield. Probably a family crest. It’s got nothing to do with children.)"

    Many speakers of English probably parse such names as something + "child", i.e. Rothschild as Roths Child. (Roth is an old spelling of rot, red.) As far as I know, I was the first person to use the term "Blumentopferd" for such mis-parsings in German. (Bonus points if you can guess what a Blumentopferd is. Hint: it is not a horse.)

  3. "Schwarzschild black holes, since they are time-reversal invariant, also necessarily come together with a white hole. Realistic black holes, on the contrary, which are formed from collapsing matter, do not have to be paired with white holes."

    This is not obvious, particularly the first sentence.

  4. Sounds like this could be a mechanism by which micro black holes dissipate once they've shrunk down to the planck scale through hawking radiation.

  5. Dear Sabine, am I wrong in thinking that the holographic principle was a solution to the Black hole info paradox? I thought it was. Really interesting post BTW.

  6. Phillip,

    Why is this not obvious? I explained previously that a time-reversed black hole is a white hole, so how can a time-reversal invariant solution with a black hole not be accompanied by a white hole? Or is it a linguistic problem in that I should better have written "The Schwarzschild solution... etc."

    My mom used to make the joke with the Blumentopferd. I was thinking of this some weeks ago when I got an email from someone telling me about a hotel "das ist Uninah" which didn't seem to exist. It took me some time to realize the word shouldn't have been capitalized, then it makes perfect sense. Best,


  7. Unknown,

    Yes, you can think of it this way. Though if the black hole has reached Planck mass, it doesn't make much difference if you think of it as a tunneling to a white hole or just some decay, period. Reason is that you'd expect the curvature fluctuations to be of order one, so even speaking in terms of classical geometries becomes meaningless.

  8. Andrew,

    The holographic principle merely tells you something about the number of degrees of freedom that can be stored within some area. It doesn't solve the information loss problem. I am guessing you were referring to the AdS/CFT duality. Most string theorists believe it solves the black hole information loss problem. However, we're not living in AdS space. Also, even in AdS space it isn't really clear just how the information escapes. The black hole firewall problem has highlighted that it isn't as easy as they thought it was. I think the whole firewall problem is a mistake, but nobody is listening to me. Best,


  9. "Karl Schwarzschild was German. Schwarz means black, Schild means shield".

    Yes. But Edmond de Rothschild was a Frenchman. The family name is derived from the German rot Schild, meaning "Red Shield".

    Thus an important question arise: Can the German Schwarzschild tunnel to the Frenchman Rothschild? :)

  10. If a black hole turns into a white hole and Emits matter does its gravitational effects remain unchanged from our POV?

  11. I explained previously that a time-reversed black hole is a white hole, so how can a time-reversal invariant solution with a black hole not be accompanied by a white hole? Or is it a linguistic problem in that I should better have written "The Schwarzschild solution... etc..

    I guess so. The way I parsed it, every black hole has an accompanying white hole, which is probably not what you meant. (Though some readers of science fiction might picture black holes leading to white holes through an Einstein-Rosen bridge, which again is probably not what you meant.)

  12. Hi Sabine

    All photons that might reach an outside observer from a region nearby black hole is redshifted, so can we view black holes as regions where all matter have the same (infinite) wavelength and thus satisfy conformal symmetry?

  13. driod33,

    That's a good question. I don't think there is a general answer to this because it's a dynamical situation. If it's a slow change you would expect that from the far distance it doesn't make a difference, the only thing that matters is the total amount of mass/energy (which better be conserved). If it has a significant dynamical component though (which it probably has at the turnaround) you would expect it to emit shockwaves. In the Rovelli/Vidotto scenario I think the assumption is that the far-away geometry is not affected. Best,


  14. tytung,

    The redshift isn't a local phenomenon, it's a global phenomenon. So is the black hole horizon. Besides this, to have conformal invariance you'd have to get rid of fermion masses. Thus the answer to your question is no. Best,


  15. Philip,

    The confusion then might be that not every black hole solution is a Schwarzschild black hole solution? Best,


  16. I understand black holes are detected by falling matter and consequent radiation. If nothing can get into a white hall, how would you ever detect it?

  17. Merger of unbound bodies into a bound body emits binding energy or no true minimum occurs. 1.74 solar-mass neutron star PSR J1903+0327 has –15.3% (AP4 model) gravitational binding energy versus Earth's -0.0000000319% (iron core). Mass falling through (POV verses LIGO external observation) a black hole event horizon loses all its mc^2?

    What is inside an event horizon, ~0% efficient filling versus 6 million solar mass local Sgr A*? A black hole is only geometry, an event horizon. The "inside" lacks description for there being none. Two Kerr black holes, 30 and 35 solar masses less three emitted, quickly merged to equilibrium because they were event horizons not volumes. Unbinding still requires binding energy insertion.

  18. kashyap,

    Well, you would see the explosion.

  19. Hi Bee,
    I see your point about explosion! But there are exploding stars and supernovas all the time. So the white hole explosion has to be of different kind!

  20. kashyap,

    Yes, it's different in that the thing that's exploding is a black hole... Also probably in other regards, but to figure that out you'd have to actually calculate something and I'm not aware of such a calculation.

  21. Dear Sabine,

    Black holes can tunnel to white holes because of spacetime torsion. They become doorways to new universes in which they look like white holes. The idea of black holes forming new universes was earlier suggested by Novikov, Pathria, and Smolin. I became interested in this scenario in 2010, when I proposed that extending general relativity to the Einstein-Cartan theory of gravity may provide a mechanism for a black hole to become an Einstein-Rosen bridge to a newly formed another universe. Such a scenario is possible because the spin of fermions, approximated as a spin fluid, produces spacetime torsion which may avoid singularities (which was found by Hehl, von der Heyde, and Kerlick in 1974).

    Here is my 2010 paper, describing this scenario and showing how it could also mimic inflation:
    "Cosmology with torsion: An alternative to cosmic inflation", Physics Letters B 694, 181 (2010).

    This scenario, with adding Zeldovich'-Parker-Starobinsky particle production near the big bounce, was found to be consistent with 2015 Planck observations (paper with S. Desai):
    "Non-parametric reconstruction of an inflaton potential from Einstein-Cartan-Sciama-Kibble gravity with particle production", Physics Letters B 755, 183 (2016)​.
    I would be very grateful if you could provide a feedback on the physical viability of this scenario.

    Nikodem Poplawski

  22. Hallo,
    some explanation to the Name Schwarzschild.
    The Origin is rather likely similar to Rothschild, but
    one has to have in mind that German "Schild" can have
    different meanings and different sex.
    "Der Schild" is part of the armour of a medieval knight,
    whereas "das Schild" is some signboard, the thing e.g.
    a butcher has outside to show the kind of his business.
    From Wikipedia:
    ""Mayer Amschel Rothschild (* 23. Februar 1744; † 19. September 1812 in Frankfurt am Main) war der Begründer der Rothschilddynastie. Seine Vorfahren hatten seit spätestens Mitte des 16. Jahrhunderts im Ghetto der Stadt Frankfurt, der Judengasse gelebt. Die Häuser in der Judengasse waren nicht durch Hausnummern, sondern durch verschiedenfarbige Schilder oder besondere Warenzeichen gekennzeichnet. Da die Familie über Generationen in dem „Haus zum Rot(h)en Schild“ wohnte, etablierte sich bereits im 17. Jahrhundert der Familienname „Rothschild“. Daran änderte sich auch nichts, als man 1664 in das „Hinterhaus zur Pfanne“ zog.""
    BTW the entry in the english Version hast the wrong translation too.
    Karl Schwarzschild was jewish and born in Frankurt, so it is more than likely
    that his Family lived in some house "zum schwarzen Schild" in the Judengasse,
    at some time maybe centuries back.

  23. @Nikodem Poplawski "Black holes can tunnel to white holes because of spacetime torsion." Given ~10^(-10) chiral anisotropic spacetime torsion background,

    1) Big Bang baryogenesis is mirror asymmetric (Sakharov conditions), creating a net matter universe.
    2) Spatial isotropy plus Noether's theorems conserving angular momentum leaks Milgrom acceleration (Tully-Fisher relationship), ending dark matter.
    3) Supersymmetry is wrong.
    4) Chern-Simons correction of Einstein-Hilbert action is sourced.
    5) Opposite shoes differentially embed within a spacetime torsion left foot. They vacuum free fall along non-identical minimum action trajectories. Eötvös experiment measure it: 4×5 g of single crystal space group P3(1)21 right-handed alpha-quartz versus 4×5 g of single crystal space group P3(2)21 left-handed alpha-quartz, 6.68×10^22 pairs of 0.113 nm^3 shoes. LOOK

  24. > Schwarzschild black holes, since they are time-reversal invariant, also necessarily come together with a white hole.

    Clearly you did not make comprehensible to Philip the meaning of this sentence and neither did u to me. As u say the perfect Schwarzschild BH is completely stationary, time enters only in the square root: therefore a time reversed Schwarzschild BH is exactly the same Schwarzschild BH, right? It has nothing to do with WHs.

    >Realistic black holes, on the contrary, which are formed from collapsing matter, do not have to be paired with white holes.

    For realistic BHs, in which some infalling matter has not crossed the event radius in our frame, yet, the point you appear to want to make in your post "WH can exist in principle but their existence would be an exceedingly unlikely fluctuation", DOES hold. In principle there could be an unlikely fluctuation that reverses the motion of all the infalling matter. Is this fact what u meant by "necessarily comes together with a WH"? If not could u explain its intended meaning?

  25. Maurice,

    The Schwarzschild solution is time-reversal invariant. It contains a black hole. Hence it also contains a white hole.

    I don't understand the rest of your comment. I am happy to hear that the point I want to make does hold.

  26. > also contains a WH

    before you wrote "comes together with a WH"
    What exactly is this supposed to mean? Again: do you agree that a time reversed Schwarzschild BH mathematically is the same BH?

    If yes, then where is its region u refer to in the following
    > a white hole contains a region to which nothing can fall in.

  27. Maurice,

    The Schwarzschild solution contains a black hole and a white hole. Most people only know that it contains a black hole. I am pointing out that knowing the solution is time-reversal invariant implies that this black hole must come together with a white hole. What exactly is this supposed to mean? It means that the Schwarzschild solution contains both a black hole and a white hole.

    "do you agree that a time reversed Schwarzschild BH mathematically is the same BH?"

    A time-reversed black hole is not a black hole. It's a white hole. Best,


  28. Just repeating statements word by word is no explanation. My second question is clearly comprehensible and to the point but u did not address it at all. Instead of answering me here, u should improve your blog post when two readers make u aware that a central statement is incomprehensible (or wrong). That's what happens high-quality blogs like Jester's.

  29. Thanks for the article. One point. There is no evidence that GR is THE 'semi classical limit'. Indeed, in the 100 years of testing, it has not failed once. The results are not all low energy - the LIGO results include very strong fields - well in excess of the electromagnetic Schwinger limit for instance.

    There is on the other hand lots of arm waving about why GR has to be a limiting case of some quantum field, but 50 years of theoretical machinations have not even found a candidate quantum field which has GR as its limit.

  30. Maurice,

    I've told you this several times before but here it goes once again: If you don't like my blog, don't read it. For some reason, you keep coming back. I wonder why.

    I handle questions about my writing by replying to them in the comments. I don't care if someone else does something different.

    Do you realize how ridiculous your insistence is that your question is "clearly comprehensible" while you complain that you're unable to understand what I have patiently explained you over and over again? If I'd lead conversations like you I would just have told you that what I have written is clearly comprehensible. But no, stupid as I am, I actually make an effort. And of course, when I try to help you, you just continue to repeat your complaints.

    I get the strong impression you're not even interested in understanding the matter.

    Phillip, in contrast to you, seems to have quickly understood my reply.

    Once again, you have merely wasted my time. You don't have to bother submitting comments for some while, bye.

  31. Tom,

    GR better be the semi-classical limit of whatever is the correct theory of quantum gravity.

  32. I admit that stating "the second question is clearly comprehensible" was dumb, and moreover you answered "no" to the previous question, so no answer was required, sorry.
    I do not comprehend the "no": Take the Schwarzschild metric of a Schwarzschild BH.
    Flip t. Nothing changes (because time only appears in dt^2). Is that correct? If no: what changes? If yes: why is it now a WH?

    Also sorry for being critical and a bit provocative, but really "if you can't take it then don't dish it out".

  33. Maurice,

    Apology accepted, thanks.

    Yes, if you time-reverse the Schwarzschild solution nothing changes - that's all I've tried to say.

    It seems to me now your confusion comes from using Schwarzschild *coordinates*. The Schwarzschild coordinates do not cover the full space-time of the Schwarzschild solution. The full space-time does (always) contain both a black and a white hole.

    Look at the first diagram in this blogpost. This is the Schwarzschild solution (full analytic extension). It has both a future and a past event horizon. It has both a black hole and a white hole. And it's the same if you turn it upside-down (which corresponds to a time-reversal).

    If you scroll down the blogpost you will also find the diagram for the collapse to a black hole, which will not remain invariant if you turn it upside down. Finally, you can have a look at this summary of Rovelli's Planck star idea that shows how the black-to-white bounce is patched together. Best,


  34. So in this connection WH is just another name for "the Schwarzschild BH in the past"?
    Or where is the WH?

  35. Maurice,

    As I said above, I don't understand your question "where" is the white hole. The Schwarzschild solution is spherically symmetric. The white hole has the same center as the black hole - otherwise how could it still be spherically symmetric? Or maybe you are asking "when" instead? The white hole, in the Schwarzschild solution, is present all the time, so is the black hole. As you noted, the metric doesn't even depend on the time-coordinate. In case you ask "where" it is in the causal diagram, the white hole is the region inside the past horizons (center bottom).

    In the black-to-white transition the situation is different. The black and white holes still have the same center, but the solution is now time-dependent by construction. As you can maybe kind of infer from Rovelli's image, you basically have to glue together a collapse with an upside-down collapse.

  36. Bee,

    " ... you'd expect the curvature fluctuations to be of order one, so even speaking in terms of classical geometries becomes meaningless."

    Only because the curvature is normalized. It should be evident that normalization of metrics can't apply in a *topological* formulation unless boundary conditions are degenerate in opposite directions, which of course standard models of cosmology assume is true. Non-disappearing torsion prevents this, in one direction. So spacetime appears flat, locally, since the observer is always subject to the cosmological initial condition of time -- which as you note in [link:] your paper [/link] which is being widely ignored, and shouldn't be -- where the observer is always sufficiently far from the origin.

    An assumed physical dualism is identical to a vacuum that separates states of nature on one physical scale from another; duality of the universe can respect one vacuum state only if it respects *all* vacuum states. This is an argument for the nonlinearity of time, and time dilation on the microscale. Entropy doesn't distinguish between past and future events.

    Joy Christian has long fought for the topological solution, gaining acceptance in top peer reviewed journals -- and while he hasn't mentioned time dependence (his solution on S^3 is complete, in the reversible Minkowski-Einstein spacetime), it is definitely implied.

    Keep pushing, Sabine!


  37. Tom,

    Sorry, I meant of order one in Planck units. Ie, of the order Planck mass squared.

  38. Bee,

    Oh, okay. Then spacetime curvature can't be degenerate in the vicinity of the mass, and classical geometries can't be ruled out?

    Here's the rub: we know that if Planck's constant is zero, the world is classical. If we normalize it to one, we are surrendering the possibility that we will ever explore below Planck scale.

    It makes more sense to me that spacetime curvature analytically continues to positive, negative or zero -- as general relativity allows -- and black hole physics accommodates all 3 forms of curvature in keeping with the general relativity indistinguishability of past and future events, and the nonlinearity of the time metric.


  39. Tom,

    I don't know what you mean by "degenerate". I also don't understand the rest of the sentence "and classical geometries can't be ruled out" since I was saying exactly the opposite: the curvature is in the Planckian regime, this means the semi-classical approximation breaks down.

    You further seem to be confusing Planck's constant with the Planck mass. Next, a choice of units has no physical relevance. Finally, curvature is a tensor, while you seem to be referring to the curvature scalar. And I have no clue what you mean by 'nonlinearity of the time metric' - there isn't any such thing as a 'time metric'. Best,


  40. Bee,

    Degenerate in this context means "A limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. For example, the point is a degenerate case of the circle as the radius approaches 0, and the circle is a degenerate form of an ellipse as the eccentricity approaches 0." (Wolfram.

    I don't like the term semi-classical, and I myself don't use it. It suggests a boundary between classical and quantum, as does Planckian regime. I think if there are regimes, they are all measure zero.

    There are units we choose, and those that are chosen for us. Spacetime is chosen for us -- which renders our own choice of units irrelevant.

    You yourself described a time metric -- " ... a timelike boundary condition in the near-horizon area and that the local observer does not notice the presence of the boundary ..."

    That is because time is dilated in the observed direction (as is confirmed by special relativity). I think you are closer to solving the information paradox than you realize.


  41. This is very confusing to me. I always understood white holes are attractive just like black holes, so how can they just be time reversed black holes?

  42. scott,

    This is correct, they are both gravitationally attractive. I think you are confusing the motion of particles in a background with the background itself.

    1. Is what you are saying this?: if you take the full analytic extension of the Schwarzschild metric you get a white hole with the black hole, then if you replace t by -t the black hole becomes a white hole and the white hole becomes a black hole.

  43. Two years later, I still find this post and subsequent discussions interesting and relevant. Thanks all.


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