enter image description here

In the drawing, A and B are two entangled particles in Kruskal coordinates, A is falling into the black hole, B is remaining outside.

The lines going through the center are the time coordinates of the far-away observer : t = 0, t = 1, t = 2, limited by the event horizon where t = $\infty$. Until the end of time t, the worldline of B is remaining outside the event horizon, and until the end of time t, the worldline of A is on its travel to the event horizon without ever reaching it.

The question: As A will never reach the event horizon, according to the time coordinates of the far-away observer how could information ever get lost from the point of view of the reference frame of an outside observer? If information is remaining outside the event horizon until the end of time, I do not see how there can be any issue of loss of information in a black hole.

Note: I am aware of the fact that the result is very different from the point of view of the infalling observer A. According to the reference frame of A, A is entangled with B until it crosses the event horizon, and at this moment it is losing suddenly the entanglement.

  • $\begingroup$ On p. 4 & 5 of a 2009 paper, titled "Radial motion into an Einstein-Rosen bridge" and visible on p. 4 & 5 of a 2009 paper titled "Radial motion into an Einstein-Rosen bridge", Poplawski provides a very technical description comparing use of Kruskal coordinates re Einstein-Rosen BH's with their use re Schwarzschild BH's, and depicts their relation in a diagram that seems very different from your own, but compatible with my answer to your question, as that answer depends on his conditions for avoidance of a singularity, which your Particle A appears to be heading straight toward. $\endgroup$
    – Edouard
    Commented Sep 20, 2021 at 19:15

2 Answers 2


$t$ is not really "the time of a faraway observer"; it's a time coordinate that anyone can use. But it's true that you can use $t$, or many other time coordinates with similar properties, to argue that there is no time at which information is unambiguously lost in a Schwarzschild black hole.

That argument doesn't work if the black hole evaporates, because the evaporation is unambiguously in your past. The information-loss paradox only dates back to the discovery of black hole evaporation, and as far as I know it has never been considered to apply to Schwarzschild and other eternal black hole solutions.

  • $\begingroup$ I'd agree that Schwarzschild (i.e, non-rotating) black holes would be phenomenally rare, but, per p.4 thru 6 of the Nobel Prize Committee's 2020 report on the award of a prize to Roger Penrose, visible at nobelprize.org/uploads/2020/10/advanced-physicsprize2020.pdf , it's evident that they're not impossible, and that, in fact, information loss might occur on any trapped surface in GR, whether that surface is spherical or not. $\endgroup$
    – Edouard
    Commented Sep 20, 2021 at 19:19
  • $\begingroup$ Sorry for the need to cut & paste the Nobel Prize URL, which I guess has to do with its publications not being intended for publication for profit. (Substituting "abs" for "pdf" didn't help, altho I'm not the best typist ever.) $\endgroup$
    – Edouard
    Commented Sep 20, 2021 at 19:23

In Nikodem Poplawski's torsion-based cosmological model (described in numerous preprints, written between 2010 and 2021, that can be found by his name on the Arxiv website), information is not lost in an absolute sense, although "we" (meaning some majority of sentient beings generally) do lose sight of it for a phenomenally long time.

His model is based on 1929's Einstein-Cartan Theory (worked out by conversations between Einstein and the mathematician Cartan, a few years after the discovery of particulate spin), rather than 1915's General Relativity. In ECT, fermions have a specified spatial extent (a few orders of magnitude greater than the Planck length) in each causal patch, whereas in GR they don't (although they are commonly considered to have some minimum size).

Perhaps so that some of the astronomical evidence which might support it would be visible, Poplawski's model is based on the gravitational collapse of large rotating stars, after the star's expenditure of its nuclear fuel would leave it without radiation pressure sufficient to resist that collapse. (There has been evidence for at least 90 such collapses, evinced by the elliptical orbit still followed by the former binary partner: A substantial proportion of stars are in binary pairs.)

In the collapse, an event horizon propagates outward from the star's center, separating the fermions of many virtual particle/antiparticle pairs from each other through extreme tidal effects, with the outer one escaping and the inner one proceeding into contact with the vastly larger stellar fermions: That contact reverses and greatly acclerates the trajectories of the fermions newly-materialized by separation from their virtual partners, and they form a new "local universe" that subsequently expands indefinitely, within and beyond the spatial volume that the "parenting" star had occupied.

Poplawki's 2010 paper described his model as an "alternative" to cosmic inflation, although it's generally considered to be a version of inflation, without a need for the hypothetical scalar "inflaton" field required in the older model developed by Guth.

So, as Poplawski would have us finding ourselves in a local universe formed by the means described, how do we regain sight of the escaped particles? By waiting through some, or even all, of the phenomenally long "Poincaré recurrence time", which was confirmed mathematically by Cathéodory in 1919. There's even a slight possibility that we might have to wait through an unspecified number of recurrences, which occur in phase space and would probably have (meanwhile) been found to have some abstruse connection with quantum uncertainty.

Because the direction of passage through relativity's time dimension would be inherited by each "baby universe" from its parent, Poplawski's theory would be confirmed by a prevalent direction of motion in a rotating region perhaps far larger than our observable one (but still within our "local universe"). Although there have been many searches for evidence of such locally-universal rotation, formulated on different bases over many years, a recent one (by Lior Shamir) does appear compatible with Poplawski's model.

Nevertheless, getting a handle on GR's multiple equations is so difficult that any generalized replacement of it by ECT (or by ECSK or ECKS, as it's sometimes known, after modifications to it that were made several decades ago by Sciama and Kibble) may occur only after some appreciable piece of the recurrence time has passed. The heartening fact that it reduces to GR in vacuum is often overlooked.

Regarding Poincaré recurrence, I have to point out that it's not limited to Poplawski's model, which I'd chosen to describe because of its avoidance of a singularity: As the local speed limit for light (which certainly applies throughout our observable region) is based on the motion of potentially massive objects with respect to each other, it can be applied to all cosmological models taking account of that spatial expansion which was first noticed by Friedmann in the early 1920's, not just Poplawski's far more recent one. Spatial expansion is not relative motion, and, as noted by Davis of Lineweaver & Davis fame, it does not cause relative motion.

  • $\begingroup$ Friedmann noticed the spatial expansion as an analytic effect of relativity: However, although the expansion's physical effect can be seen by anyone noticing that the night sky is not a sheet of fire, the astronomical evidence for it is usually considered to be that redshift (of starlight) which was discovered by Hubble's assistant Slipher. $\endgroup$
    – Edouard
    Commented Sep 20, 2021 at 6:53
  • $\begingroup$ Participants reading my answer might want to look at my comment on the OP's question, for a reference technical enough that I'd have to describe it verbatim. $\endgroup$
    – Edouard
    Commented Sep 20, 2021 at 8:38
  • $\begingroup$ An avoided singularity differs from a singularity that doesn't exist: However, the only massive objects in his scenario that don't avoid the singularity, as far as I can infer from the English verbiage in Poplawski's descriptions, would be the fermions of the collapsing star, that would consequently fail to deter the expansion of the local universe formed by the newly-materialized fermions (evidently on a smaller scale) comprising it, whose gravitational potential, causally-separated, would consequently leave the new LU free to expand outward. $\endgroup$
    – Edouard
    Commented Sep 21, 2021 at 17:47
  • $\begingroup$ Those "massive remnants" of a star in the "parenting" LU would not be accessible to whatever beings might eventually evolve in the new, outward-expanding LU (whose shape Poplawski has analogized to the skin of a basketball), as they would exist in a time preceding its formation. $\endgroup$
    – Edouard
    Commented Sep 21, 2021 at 18:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.