Albert Einstein’s theory of gravity general relativityis famously incomplete. As proven by the Nobel Prize winner in physics Roger PenroseWhen matter collapses under its own gravity, the result is a ‘singularity’ – a point of infinite density or curvature.





At a singularity, space, time and matter are crushed and stretched into non-existence. The laws of physics as we know them are undergoing a complete collapse.





If we could observe singularities, our physical theories could not be used to predict the future from the past. In other words, science would become an impossibility.





Penrose also realized that nature could provide a remedy for this fate – black holes.





A defining characteristic of a black hole is the event horizon, a one-way membrane in space-time. Objects – including light – that cross the event horizon can never leave due to the black hole’s incredibly strong gravity.





In all known mathematical descriptions of black holes, singularities are present in the core.





Penrose postulated that all gravitational collapse singularities are ‘clad’ by the event horizon of black holes – meaning we could never observe one. With the singularity within the event horizon, physics in the rest of the universe is ‘business as usual’.





This Penrose conjecture, that there are no ‘naked’ singularities, is mentioned cosmic censorship.





After half a century it is still unproven and one of the most important open problems in mathematical physics. At the same time, it has proven equally difficult to find examples of cases where the presumption does not hold.





In recent work, published in Physical Assessment Letterswe have shown that quantum mechanics, which governs the microcosm of particles and atoms, supports cosmic censorship.


First black hole in the picture
First ever image of a black hole. (Event Horizon Telescope/Wiki Commons, CC BY-SA)

Black holes


Black holes are influenced by quantum mechanics to some extent, but physicists normally ignore this influence. For example, Penrose ruled out these effects in his work, as well as the theory that allowed scientists to measure ripples in space-time, called gravitational waves from black holes.





When included, scientists call the black holes “quantum black holes.” These have long created even more mystery, because we don’t know how the Penrose conjecture works in the quantum world.





A model in which both matter and space-time follow quantum mechanics is often considered the fundamental description of nature. This could be one “theory of everything” or a theory of “quantum gravity”.





Despite tremendous efforts, an experimentally verified theory of quantum gravity remains elusive.





It is widely expected that any viable theory of quantum gravity would have to resolve the singularities present in the classical theory – potentially showing that they are simply an artefact of an incomplete description. So it is reasonable to expect that quantum effects will not exacerbate the problem of whether we can ever observe a singularity.





That’s because Penrose’s singularity theorem makes certain assumptions about the nature of matter, namely that matter in the universe always has positive energy.





However, such assumptions can be violated quantum mechanically – we know that negative energy can exist in small amounts in the quantum realm (so-called Casimir effect).





Without a fully-fledged theory of quantum gravity, it is difficult to answer these questions. But progress can be made by taking into account ‘semi-classical’ or ‘partial-quantum’ gravity, where space-time obeys. general relativity but matter is described by quantum mechanics.





Although the governing equations of semi-classical gravity are known, solving them is a completely different story. Compared to the classical case, our understanding of quantum black holes is much less complete.





From what we know about quantum black holes, they also develop singularities. But we expect that a suitable generalization of classical cosmic censorship, namely quantum cosmic censorship, would exist in semi-classical gravity.





Developing quantum cosmic censorship


As yet, there is no firm formulation of quantum cosmic censorship, although there are some clues.





In some cases, a naked singularity can be modified by quantum effects to obscure the singularities; they become quantum clothed. That’s because quantum mechanics plays a role in the event horizon.





The first example was presented by physicists Roberto Emparan, Alessandro Fabbri and Nemanja Kaloper in 2002. Now all known constructions of quantum black holes share this feature, suggesting that a more rigorous formulation of quantum cosmic censorship exists.





Closely linked to cosmic censorship is the Penrose inequality. This is a mathematical relationship that, assuming cosmic censorship, says that the mass or energy of space-time is related to the area of ​​the black hole horizon contained within it.





Consequently, a violation of the Penrose inequality would strongly indicate a violation of cosmic censorship.





A quantum Penrose inequality could therefore be used to rigorously formulate quantum cosmic censorship. One team of researchers proposed such an inequality in 2019. Although promising, their proposal is very difficult to test on quantum black holes in regimes where quantum effects are strong.





In our work we discovered a quantum Penrose inequality that applies to all known examples of quantum black holes, even in the presence of strong quantum effects.





The quantum Penrose inequality limits the energy of space-time in terms of its total entropy – a statistical measure of a system’s disorder –
of the black holes and the quantum matter contained within them. This addition of quantum matter entropy ensures that the quantum inequality remains true even if the classical version breaks down (on quantum scales).





That the total energy of this system cannot be lower than the total entropy is also natural from the point of view of thermodynamics. To avoid a violation of the second law of thermodynamics – that the total entropy never decreases.





When quantum matter is introduced, its entropy is added to that of the black hole, satisfying a general second law. In other words, the Penrose inequality can also be understood as limits on entropy – if you go beyond this limit, space-time develops naked singularities.





On logical grounds, it was not obvious that all known quantum black holes would satisfy the same universal inequality, but we have shown that this is the case.





Our result is not evidence of a quantum Penrose inequality. But the fact that such a result holds in both the quantum domain and the classical domain strengthens it.


Although space and time can end in singularities, quantum mechanics shields this fate from us.The conversation


Andreas SveskoResearch associate in theoretical physics, King’s College London; Antonia Micol FrassinoResearcher, Scuola Internazionale Superiore di Studi Avanzati; Juan F. PedrazaResearch Associate at Instituto Fisica Teorica UAM/CSIC, Universidad Autonoma de MadridAnd Robie HennigarWillmore Fellow of Mathematical Physics, University of Durham


This article is republished from The conversation under a Creative Commons license. Read the original article.



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