flat space

An orchestra of a hundred musicians plays without a conductor. Every instrument is tuned perfectly, but one violin goes slightly off, and the harmony falls apart.

Imagine an interferometer as a giant ear listening to the radio whisper of a distant galaxy. Three antennas spread across continents capture the signal, and the difference in their phases combines into a quantity that is immune to atmospheric jitter. This quantity is called the closure phase.

An ordinary mirror swaps left and right. Many laws of physics don't notice the swap: they are mirror-symmetric. But some phenomena, like the weak interaction, break this symmetry. Until now, it was thought that gravity and light each break mirror symmetry in their own independent way.

Think of a merry-go-round: the farther you sit from the center, the faster you're carried around. For a long time, astronomers assumed galaxies work the same way — stars at the edges should orbit more slowly than those near the center. But back in the 1970s, it turned out that in many spiral galaxies, the speed of stars barely drops with distance from the center.

Two tiny diamonds float in a vacuum, separated by a distance that light cannot cross during the experiment. Inside each, like a frozen spark, resides an entangled spin — a quantum state linking them into a single whole. Now the diamonds begin to move, but not just any motion: each one seems to split, existing in two places at once.

A spotlight beam fades into the darkness, but if you trace it backward, you hit the lamp. The history of the universe might be the same: tracing its expansion backward, we run into a beginning. Physicists took the simplest model — a universe that stretches equally in all directions, like a cube with all sides growing.

A black hole is not just a dark spot in space. It has a temperature, and it radiates. It has entropy — a measure of hidden information encoded on its horizon's surface, like a pattern on a soap bubble.

Newton gave us a world where bodies move in a void and clocks tick the same for everyone. For three centuries, this picture worked flawlessly. But it relies on many invisible props: absolute position, the 'up-down' direction, and a single rhythm of time for the entire universe. We have never measured these directly — only through the relations between objects.

Two massive bodies frozen in a quantum superposition resemble a pair of dancers trying to keep a single rhythm while an orchestra blares around them. Each gravitational wave is a musician throwing them off beat.

The idea was elegant: take a BTZ black hole (the three-dimensional analog of a regular black hole) and smooth its horizon with a special function. The hope was that inside, the spacetime signature might change — time becoming space, and space becoming time. But the calculations showed otherwise.

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 thrown stone arcs through the air and falls. A planet orbiting a star is the same stone, but it falls forever, looping around the star in a closed curve. In Newton's world, that curve is a perfect ellipse, and the planet returns to the same point each orbit. In reality, the orbit slowly rotates: its closest point to the star, the perihelion, shifts.

Two houses with identical facades. Windows, doors, wall color — everything matches. But inside, one is empty, while the other buzzes with life. How can you tell without stepping inside? In space, there's a similar puzzle: a black hole and a gravastar look the same from the outside, but they are built differently.

A pendulum in a noisy room is constantly jostled by people passing by. Its motion is a mix of regular swings and random jerks. Something similar happens with weak gravitational waves against the backdrop of an expanding universe. In Einstein's general relativity, these waves are tiny ripples in spacetime.

The early universe was less like a calm pond and more like a boiling cauldron. Matter flowed, collided, and swirled against the backdrop of rapid spatial expansion. To understand how stars and galaxies emerged from this hot soup, physicists build digital simulations. This new work is the third part in a series on lattice-based cosmological modeling. The first two focused on fields; this one deals with fluids.

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.

Two cities with the same average population density. In one, a neat grid of blocks; in the other, a maze of narrow alleys and unexpected squares. On a global map they look like twins, but life inside flows quite differently.

In the quiet of the quantum world, there is no emptiness. Particles are intertwined by invisible threads — entanglement. The authors of the work proposed that the very fabric of spacetime is woven from these threads. This is not just a metaphor: they built a mathematical framework where the distance between points is determined by how much shared information they hold.

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.

The Standard Model of particle physics is a catalog of all known building blocks of the universe: electrons, quarks, and others. But it is silent about dark matter and doesn't get along with gravity.

Usually, a black hole is described as a frozen frame: there's mass, there's charge, and it's all static. But real objects live in time. They radiate, lose energy, and change.

An eardrum at the very edge of a waterfall. Sound behaves strangely here: echoes don't multiply: they fade. That's exactly what gravitational waves look like at the horizon of a black hole — the boundary beyond which even light disappears.

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.

Imagine a pot of boiling water. Toss in a handful of pasta, and it quickly overcooks and clumps into a sticky mess. But in a huge restaurant kettle where the pasta floats freely, each piece stays separate.

At the center of attention is a black hole of unusual shape. Its geometry resembles a spindle: a slight elongation is added to the usual rotation. The parameter B measures this deformation. The spindle deformation is not just a mathematical toy.

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.

Two light rays meet at a point and then diverge. Their paths form two intersecting surfaces in spacetime — null hypersurfaces (boundaries along which light propagates). It is on such a pair of surfaces that physicists can set initial data for Einstein's equations. This is called the characteristic Cauchy problem.

Two synchronized swimmers dive into the sea. One hits calm water, the other a whirlpool. Their movements, perfectly coordinated at the start, diverge. Something similar happens to two quantum particles when one moves in flat space and the other in curved space.

In cricket, there's a special delivery — the googly. The ball spins in a way that deceives the batsman. Physics had its own googly: for nearly half a century, mathematicians couldn't make twistor theory work with real gravity. It described 'nice' fields perfectly, where everything twists in one direction. But as soon as an 'awkward' component appeared, the machinery broke down.

In the first moments after the Big Bang, the universe expanded at a terrifying rate. This process is called inflation, and it smoothed out all the wrinkles, making the cosmos homogeneous. But what started inflation itself?

A quantum wave is like a long-exposure photograph: everything’s blurred, but the blur itself reveals motion. Usually these frozen waves are treated as convenient abstractions. Yet if at each point in the image you estimate, by brightness, the moment on the particle’s internal clock it landed there, flat space suddenly acquires curves.

A translator who translates not words but the very structure of a conversation runs into trouble when the chat moves beyond a quiet room. In a familiar simulation on a spatial lattice, everything follows a strict script. But the moment the interlocutors find themselves in a noisy square, where sound is distorted by echoes and the crowd keeps changing direction, the script falls apart.

At the center of a black hole, classical theory paints a point where density and spacetime curvature shoot to infinity — like an infinitely sharp needle. But quantum corrections, tracing back to the work of Karl Schwarzschild, add a tiny “pillow”: space cannot collapse to zero.

Dim the lights. The stage belongs to a shadow theater, with just r puppeteers, but the screen obeys the laws of hyperbolic geometry. Every wave of the hand births a pattern that mathematicians call a discrete group of isometries.

In the ocean, a whirlpool pulls everything into a closed loop, just as a gravitational wave in empty space twists time into a loop. Gravitational wave — a ripple in the fabric of spacetime, and its special shape can turn the usual flow of events into a closed cycle. In such a zone, an object can return to its own past without violating the laws of physics.

A textbook black hole resembles a perfectly smooth sphere: everything outside it calmly flies off to infinity. However, quantum gravity paints a different picture. Recently, within loop quantum gravity, a solution was found — a 'Kruskal' black hole where spacetime beyond the horizon behaves differently.

An object cannot be a point. At least, not in Einstein's gravity. The equations of general relativity require that the source of the field, matter, be smeared out in space, not concentrated in an infinitesimal volume. Otherwise, infinities appear in the formulas, and a smooth spacetime cannot be constructed.

Building a house on sand is a bad idea. In physics, it was long believed that a quantum theory of gravity could not be built on a fixed "sand"—a pre-existing spacetime.

A ball sits in a pit. It won't roll out on its own: it needs a push. But in the quantum world, a particle can leak through a barrier without extra energy. This trick is called tunneling.

The boundary sets the rules Quantum gravity is like a theater where spacetime is the stage and fields are the actors. When the stage has an edge, you need to know exactly what happens at the boundary; otherwise, the play falls apart. In 2018, Edward Witten proposed an elegant recipe for such a case.