Numerical simulations have pointed physicists to the region of black holes where the predictability of physical laws must be violated. In such a region, the subsequent states of the system may not be a consequence of the current ones, which is impossible in Newtonian mechanics and classical electrodynamics. An article with the results was published in the journal Physical Review Letters.
Usually physical theories speak about the determinism of the world, the predictability of the future: if the initial conditions are known, then, knowing the physical laws, one can calculate the state at any moment in the future. Such a theory, for example, is Newtonian mechanics. The same is true for classical electrodynamics: knowing exactly the distribution of electric and magnetic fields in space, you can determine their state at any other moment using Maxwell's equations. Even in quantum mechanics, the Schrödinger equation does not allow for randomness: if we know exactly the wave function at the initial moment, then it unambiguously speaks of its time evolution at any time interval.
In the new work, a group of theorists led by Vitor Cardoso from the University of Lisbon examines the collapse of a charged star into a black hole and models this phenomenon within the framework of general relativity. As a result, it turns out that in this process a region may arise, the physics of which cannot be predicted by knowing the initial state of the star.
According to one of the theorems within the framework of general relativity, there is a maximum region of space-time that is uniquely determined by these initial conditions. If this area is not the entire existing space, then by definition it turns out that there are areas whose state is not determined by the initial conditions taken. The English scientist Roger Penrose formulated a hypothesis that was called the principle of strong cosmic censorship. He argues that this cannot happen, that is, an unambiguous definable area is not part of some larger space.
The formation of a charged black hole, described by the Reissner-Nordstrom metric, violates this principle at first glance, since in this case the Cauchy horizon is formed inside the black hole, to which space-time remains smooth, and beyond it can be extended in an infinite number of ways. But on the other hand, this surface is unstable and any disturbance destroys it, leads to the formation of a singularity and justice of the principle of cosmic censorship.
The new work investigates the collapse of a star into a black hole with a near-limiting charge taking into account the cosmological constant (Λ-term in Einstein's equations). The Λ term is very small and is usually taken into account only in cosmological studies, but it has been shown that a positive value of Λ leads to a more stable Cauchy horizon. As a result, even taking into account the perturbations, the discrepancy between the space-time parameters on the Cauchy horizon is not large, which makes it possible to solve the Einstein equations even at the very horizon. This violates the principle of strong cosmic censorship.
The curvature discontinuity at the Cauchy horizon obtained in the situation of a limiting charge and a positive Λ-term is similar to a shock wave in a liquid. It turns out that a sufficiently strong body could penetrate through it. One can imagine an observer jumping into a black hole and crossing the Cauchy horizon. In this case, his future turns out to be uncertain.
The proof of the validity of the analysis performed is still required, since the authors considered only the linear perturbation theory. It is also worth noting that astrophysical black holes with limiting charges cannot form, since there are no such highly charged stars. However, the Cauchy horizon also appears in the case of rotating black holes, although they have fewer symmetries. Also, the work did not take into account hypothetical quantum effects, which can be strong in such areas.
Promotional video: