Some black holes blur the traveler's past, but reveal an infinite number of options for the future.

Chronological future for point p

The behavior of small perturbations of the gravitational and electromagnetic fields inside a black hole is a long-time subject of research in the General Theory of Relativity (GTR). We need to know very precisely how these perturbations are damping in order to advance in understanding the nature of gravity, from interpreting data from registered gravitational waves to more fundamental issues, such as the deterministic nature of GR.

The appearance of the Cauchy horizon in astrophysical applications of Einstein’s calculations indicates a possible violation of determinism in the framework of GR. As is well known, the Cauchy horizon limits the “region of predictability”: Beyond the Cauchy horizon, unambiguous predictions are impossible in either classical or quantum theory, since some of the necessary information comes from other regions of spacetime that do not intersect with Cauchy’s initial partial surface.

In other words, we can no longer predict the future of an observer who crosses the Cauchy horizon, based on the initial conditions before the intersection of the horizon and the Einstein equations. However, in the context of black hole (BH) space-time, it can be expected that the perturbations of the outer region can be infinitely enhanced, turning the Cauchy horizon from the inside into a singularity (finite boundary), beyond which the field equations no longer make sense. This assumption is justified in the Penrose hypothesis about the principle of "space censorship . "

Penrose formulated the principle as follows: "Nature has an aversion to the bare singularity." This means that the space-time singularities appear in such places, which, like the inner regions of black holes, are hidden from observers.

A group of mathematicians from the University of California at Berkeley, the Perimeter Institute for Theoretical Physics (Canada), the Institute for Theoretical Physics and the Center for Extreme Matter and Emergent Phenomena from the University of Utrecht (Netherlands) published a scientific paper that explains that the principle of "space censorship" is directly related with how strongly the outer boundary of the Cauchy horizon suppresses perturbations of the gravitational and electromagnetic fields. An analysis of the nature of these attenuations makes it possible to guess what is happening on the inner boundary of the Cauchy horizon, where the singularity is manifested - and what this means for the traveler who gets there.

Specifically, the scientists studied the massless scalar fields outside the black holes in the Reisner – Nordström model for the de Sitter space, that is, for the relativistic cosmological model. Their decay rate is determined by the quasinormal black hole modes. Of course, measurements of physical characteristics beyond the horizon of events are carried out by purely mathematical methods: “No physicist can get into a black hole and measure it,” said Peter Hinz from Berkeley, one of the authors of the scientific work. - This question can really be studied only mathematically, but it has physical, almost philosophical consequences. From this point of view, Einstein’s equations become mathematically more interesting. ”

The authors of the scientific work identified three families of modes in these space-times. One family is directly related to the photon sphere and is well described. The second type of mode is closely related to the de Sitter horizon by its existence and time scale. Finally, the third family dominates in almost extremely charged black holes — and it also exists in asymptotically flat variants of spacetime.

The authors say that the last two versions of the modes seem to have gone unnoticed in the existing literature on the physics of black holes. Therefore, in their work, they gave a detailed description of the scalar perturbations of such BHs and the rationale for the hypothesis that the principle of “cosmic censorship” is violated in the BH variant with a charge close to the extreme one.

What does the violation of the principle of "cosmic censorship" in these black holes mean? This means that some singularities may be available to an external observer - albeit with strange consequences for it.

According to the simulation, when penetrating into such a theoretical black hole, the observer will not cease to exist, but his past will be erased. In addition, it will open to a potentially infinite number of possible options for the future, like the owner of the Sword of Probability from the fantasy novel "The Scar" of China Myvil.

The observer will never be able to come out of the black hole and tell his story, but it does not matter, because no one from the past will exist anymore, nor will the past itself.

The scientific article was published on January 17, 2018 in the journal Physical Review Letters (doi: 10.1103 / PhysRevLett.120.031103, pdf ).