Water, at precisely zero degrees, is uncertain about what it aspires to be. Introduce the slightest hint of energy and it remains a liquid; take away the same and it transforms into ice, with molecules forming a perfect repeating lattice. That pivotal moment of indecision, that delicate threshold, is its own peculiar kind of entity. For many years, physicists speculated that a similar phenomenon could occur with spacetime. Not water molecules, but the very essence of the universe, arranging itself into a crystal-like pattern right at the brink of becoming a black hole. Now, for the first time, a group from Vienna and Frankfurt has recorded an exact mathematical depiction of what that entity looks like, using nothing but paper and pencil.<\/p>\n
The outcome, published in *Physical Review Letters*, addresses an issue that has remained unresolved since 1993. It also uncovers something truly peculiar regarding the formation of black holes, and suggests what the early universe might have resembled.<\/p>\n
The narrative begins with a physicist named Matthew Choptuik, who in 1993 was conducting computer simulations of collapsing matter. He discovered that if you adjust the energy of an infalling shell of particles to a critical threshold, the boundary between \u201ccollapse to a black hole\u201d and \u201cdisperse harmlessly,\u201d the resulting spacetime does not merely remain still. It pulses. It oscillates with a specific repeating rhythm, demonstrating a discrete self-similarity, as if spacetime itself were a crystal possessing a regular lattice structure. Physicists referred to this condition as critical collapse, and they quickly recognized that it bore the characteristics of a phase transition, akin to the moment when water freezes into ice. The analogy was powerful; however, the mathematics involved was exceedingly complex.<\/p>\n
For 33 years, Choptuik\u2019s critical solution existed solely in numerical form, something that computers could approximate but no human equation could encapsulate. \u201cSometimes a tiny, seemingly inconsequential cause is enough to instigate a massive and dramatic change,\u201d states Prof. Daniel Grumiller of TU Wien, one of the contributors to the new research. His ice analogy is fitting. Yet while the physics of water freezing can be expressed in relatively manageable equations, the equations governing spacetime near a black hole threshold are (to put it mildly) not.<\/p>\n
The method employed by the Vienna-Frankfurt team to unlock this is, at first glance, absurd. Our universe has four dimensions: three of space and one of time. The equations of general relativity in four dimensions do not easily simplify; there\u2019s no small number to expand around, no obvious approximation method to exploit. But what if you allowed the number of dimensions to increase? Not to five, or forty-two, but all the way to infinity. As Christian Ecker of Goethe University Frankfurt notes, nothing in principle inhibits you from formulating the equations for any number of dimensions, five, or forty-two, or infinitely many. The equations in that limit, oddly, simplify into something much more manageable. The four-dimensional dilemma, reimagined as the infinite-dimensional limit of a broader theory, succumbs to analytical techniques that were simply inaccessible before.<\/p>\n
What they uncovered in that limit is an entire family of exact solutions, an infinite catalog of spacetime crystal configurations, each defined by a singular function of time encapsulating the repeating rhythm of the structure. The solutions are, by the metrics of general relativity, exceptionally clear. \u201cOur technique turns out to be remarkably stable,\u201d remarks Florian Ecker of TU Wien. \u201cDepending on the required precision, we can systematically refine our formulas using additional approximation techniques. This provides us with a new approach for examining black-hole-related phenomena that could not previously be analyzed analytically.\u201d<\/p>\n
The \u201ccrystal\u201d designation is more than just a metaphor. In a conventional crystal, atoms are positioned at regularly spaced points; disturb the lattice and it either persists or shatters. The Choptuik spacetime crystal exhibits a similar duality. \u201cIt represents a sort of intermediate state, an unstable point that can evolve in two different ways,\u201d explains Grumiller. \u201cIt may simply disintegrate again, leaving behind ordinary spacetime filled with freely moving particles. But if a slight amount of energy is introduced, the evolution takes an entirely different trajectory: the unassuming spacetime crystal transforms into a black hole.\u201d The crystal is, in this respect, a universe teetering on the edge of a pin.<\/p>\n
To extract useful information from the infinite-dimensional solution regarding our unmistakably four-dimensional universe necessitates bringing it back down through a series of corrections. The team navigated through the leading-order solution (clean yet imprecise), then next-to-leading order, followed by the level beyond that. Each correction encapsulates more of the structure evident in Choptuik\u2019s initial numerical simulations, including the curvature of specific geometric features known as null energy condition lines, which remained obstinately incorrect until the second correction was incorporated. There\u2019s something almost perverse about this method: the universe.<\/p>\n","protected":false},"excerpt":{"rendered":"
Water, at precisely zero degrees, is uncertain about what it aspires to be. Introduce the slightest hint of energy and it remains a liquid; take away the same and it transforms into ice, with molecules forming a perfect repeating lattice. That pivotal moment of indecision, that delicate threshold, is its own peculiar kind of entity. […]<\/p>\n","protected":false},"author":2,"featured_media":372674,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"Default","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[179],"class_list":["post-372673","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized","tag-source-scienceblog-com"],"_links":{"self":[{"href":"https:\/\/wolfscientific.com\/index.php?rest_route=\/wp\/v2\/posts\/372673","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wolfscientific.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wolfscientific.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wolfscientific.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/wolfscientific.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=372673"}],"version-history":[{"count":0,"href":"https:\/\/wolfscientific.com\/index.php?rest_route=\/wp\/v2\/posts\/372673\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wolfscientific.com\/index.php?rest_route=\/wp\/v2\/media\/372674"}],"wp:attachment":[{"href":"https:\/\/wolfscientific.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=372673"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wolfscientific.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=372673"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wolfscientific.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=372673"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}