singularity

In 1934 Jean Leray proved that the Navier–Stokes equations always have solutions "in a generalized sense". Whether a solution stays smooth or can break down into a singularity he could not tell, and nobody could for ninety years. In 2000 the Clay Institute made the question one of its seven Millennium Prize problems.

A thin film of zirconium nitride lies on a magnesium oxide substrate. Its thickness is two-tenths of a micron, like a spider's web, but inside it quantum life is boiling. When cooled to half a kelvin, superconductivity does not disappear all at once: it breaks up into rare islands that still hold on amid the disorder.

Drop a pebble into a pond, and ripples spread across the water. Something similar happens when a black hole merges with another: it emits gravitational waves that resemble the fading ring of a bell.

When two heavy balls merge into one, ripples spread across the water's surface for a long time. A black hole behaves similarly: after a merger, it 'rings' for a while, emitting special gravitational oscillations — quasinormal modes. Usually, this ring fades quickly, like an echo dying out in an empty hall.

A homogeneous, spherical cloud of cosmic dust begins to contract under its own gravity. At some point, by classical laws, it should collapse into a point of infinite density — a singularity.

The universe isn't just a place; it's a schedule of events: what happened earlier and what happened later. In Einstein's geometry of spacetime, this schedule sometimes breaks off. For instance, inside a black hole, particle paths run into a singularity — an edge beyond which the equations stop.

In the far reaches of space, there exists a hypothetical object: an ultracold black hole. It is charged and resides in an expanding universe (de Sitter space). Its temperature hovers just above absolute zero — about one trillionth of a degree above it.

A scale that weighs not a body, but the very space around it. That's how Einstein's equations work in general relativity: they link the curvature of spacetime to what resides within it.

A black hole spun up almost to its limit is like an athlete balancing on the edge of a record. The most interesting action isn't inside the hole itself, but in the thinnest film of spacetime at its horizon. It's there that tiny corrections to Einstein's gravity can suddenly swell to gigantic proportions.

A black hole's shadow isn't just a black circle. Usually, we see a dark void surrounded by a glowing ring of hot gas. But if a black hole wasn't born from a dying star but has existed forever, its shadow might hide a surprise. An eternal black hole is a solution to Einstein's equations with no past and no collapse.

A classical black hole is a bottomless well: everything that falls past the horizon disappears into a point of infinite density. But in loop quantum gravity (one approach to quantum gravity), that point is replaced by a quantum 'bounce'—a sphere of finite size where spacetime doesn't tear but rearranges itself.

The holographic principle is often compared to a hologram: all the information about a volume is encoded on a flat surface. In physics, this means that three-dimensional spacetime with gravity could be equivalent to a two-dimensional theory without gravity — a so-called conformal field theory (CFT).

The quantum world is a constant buzz of activity. Particles exchange energy, become entangled, and influence one another. You'd think that the more players in this game, the harder it is to predict the outcome. But sometimes, order emerges from chaos. Physicists took a close look at the SYK model — a mathematical playground for studying quantum chaos.

The universe sometimes resembles an old fabric: after rapid cooling, wrinkles could have remained — thin, almost invisible threads of monstrous density. They are called cosmic strings. Usually, at the center of such a string hides a singularity — a point where the laws of physics lose their meaning.

A rotating black hole is no calm whirlpool. Space around it shudders and rings at the slightest disturbance, like a guitar string after a pluck. These oscillations are described by the Teukolsky equation — a complex mathematical construct that physicists have studied for half a century. Recently, a strange symmetry was noticed in this equation.

An old house. The facade is freshly painted, the stairs don't creak. A pretty picture. But try to move in heavy furniture, and the floorboards give way. The beauty of the facade says nothing about the strength of the floors. It's much the same with black holes without singularities.

The Kerr-NUT black hole is not just a cosmic vacuum cleaner. It's a solution to Einstein's equations where the hole has mass, rotation, and a strange NUT parameter. This parameter behaves like a magnetic charge for gravity: seemingly invisible, yet it alters the properties of surrounding space.

In the familiar picture of the world, an event is a point on the map of spacetime: 'here and now,' with no size or internal structure.

Light freezes at the edge of the abyss: that's what the event horizon of an ordinary black hole looks like. But at the center of this abyss lurks a singularity, a point where the laws of physics break down. What if, instead of a point, there were a hard shell? A gravastar is not a black hole.

A cloud of waves collapses under its own gravity. While it's loose, everything goes by the book: the field oscillates gently in nearly flat space, and approximate formulas work perfectly. But add just a bit more energy, and the picture changes. Physicists used a numerical model to catch the moment when simple calculations stop describing reality.

A stone falls into still water — ripples spread across the surface. A black hole behaves similarly when something falls into it or when it merges with another black hole. The hole begins to oscillate, and these oscillations propagate through space as gravitational waves.

At the center of nearly every galaxy lurks a supermassive black hole. Its gravity is so strong that it warps space itself. But few stop to wonder: what does it do to the very fabric of reality — the fields that permeate the cosmos? One such field is the Higgs field.

An engineering blueprint of a skyscraper always includes a number: the maximum load on the foundation — say, 500 kilopascals. Einstein's field equations in curved spacetime impose a similar limit on the 'force load' inside stars, planets, and any other clumps of matter.

An engineering blueprint of a skyscraper always includes a number: the maximum load on the foundation — say, 500 kilopascals. Einstein's field equations in curved spacetime impose a similar limit on the 'force load' inside stars, planets, and any other clumps of matter.

Hot tea cools down, a pendulum comes to rest — nature loves equilibrium. But a charged black hole can reach a special, extreme state: the mass becomes minimal, and the temperature drops to zero.

Water turns to ice at zero degrees — sharply, with no intermediate states. Something similar happens to complexity when we take a random quantum state of an entire system and look only at a part of it. As long as that part occupies less than half the system, its complexity grows smoothly. But as soon as the fraction crosses 50%, a jump occurs.

A light ray skimming along a black hole horizon doesn't just move: it carries heat and information. Physicists have long suspected that the geometry of such rays obeys strict rules, but the details remained blurry. The new work turns these rules into a sharp inequality.

The spiral of water draining into a sink spins faster and faster toward the center. In an ordinary black hole, that funnel ends in an infinitely sharp point — a singularity where the laws of physics break down. But this new work considers a different picture: the funnel doesn't taper to a needle but ends in a smooth, swelling bubble.

A campfire burns steadily and long. But when the wind blows, the flame flickers out, leaving only embers. A similar story plays out with the gravastar — a hypothetical object that was supposed to replace the black hole. An ordinary black hole hides a singularity — a point where the laws of physics break down.

A huge bowl of water. Drop a stone into it — ripples spread across the surface. The fabric of spacetime works much the same way: when two massive stars merge, they create ripples — gravitational waves. These waves travel to Earth and are picked up by giant detectors like LIGO and Virgo.

At the center of many galaxies lurks a black hole, wrapped in an invisible cloud — the halo of dark matter. This is not just a featureless mass: its density changes from the edge to the center, and the degree of this "compression" is called compactness.

A star runs out of fuel and rapidly collapses under its own gravity. According to classical ideas, it collapses into a point of infinite density — a singularity. But what if nature abhors infinities? In models of regular black holes, instead of a singularity, a dense core of unknown matter forms at the center.

A black hole usually hides its singularity behind an event horizon — an invisible boundary from which not even light can escape. But sometimes this 'cloak' is absent, and the singularity, a point where familiar physics breaks down, is exposed to an outside observer.

An ordinary black hole hides a singularity at its center — a point where density and curvature become infinite and the laws of physics break down. The authors of the new work built a model of a rotating black hole that, instead of a singularity, contains a calm "core" resembling ordinary flat space.

A stone drops into a pond — ripples spread and fade. Strike a bell, and it hums at its own pitch. A black hole, after being perturbed, also 'rings,' emitting gravitational waves of a decaying tone.

A clay ball is kneaded in your hands, changing shape but not tearing — some parts stretch, others compress. That's roughly how physicists work with spacetime, except their fingers are equations and their clay is a six-dimensional world.

At the center of a classical black hole lurks a singularity — a point where the density and curvature of spacetime become infinite. Physics goes silent there.

Hot gas spirals inward, falling onto an invisible superdense object. Such a disk resembles a giant whirlpool, but it is often tilted: its axis does not align with the rotation axis of the central body. The gravity of the massive object makes the disk wobble slightly, like a spinning top losing its balance.

At the center of an ordinary black hole, according to classical ideas, lurks a singularity — a point of infinite density where the laws of physics break down. But some theories, inspired by the duality idea from string theory, propose replacing the point with a tiny 'smudged' region.

In classical theory, a black hole is where matter collapses to a point of infinite density. Such a 'singularity' looks like an error in the equations: nature hardly tolerates infinities. Many physicists seek ways to 'smooth out' this flaw, and one idea is to modify the theory of gravity itself at small distances.