anti de sitter space

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.

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 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.

After a hit, a black hole rings like a bell. But instead of sound, it emits gravitational waves whose frequency rapidly decays: these are called quasinormal modes. From such a 'ring,' you can infer the hole's mass, spin, and other properties.

Two balls dropped from different heights fall to the ground with different accelerations. In space, things are more complicated: even emptiness makes bodies move differently.

An inflatable balloon with magnetic field lines drawn on it with a marker is a simple model of how a weak magnetic field behaves in an expanding universe. While the balloon is small, the lines lie obediently on the rubber and don't hinder its stretching. That's roughly how a field fills ready-made space without arguing with its geometry.

Gas passing through a narrow valve can heat up or cool down: this is the Joule–Thomson effect, which powers refrigerators and air liquefiers. It turns out black holes can do the same.

The universe is a grand orchestra, with dark energy conducting the expansion. Ten billion years ago, the conductor changed its gesture: the negative pressure that had been holding back galaxy assembly gave way to accelerating expansion — the very phenomenon discovered by [scientist:Saul…

In the ordinary world without dark energy, the mass of any object is always positive. That seems obvious: positive mass attracts, creating gravity. But the real universe has dark energy — a mysterious force making the cosmos expand faster and faster.

The boundary of a black hole is like the edge of a waterfall: cross it, and there's no way back. But unlike a waterfall, this boundary can be very fragile: a light nudge is enough to make it vanish. Physicists have found that the horizon's stability is set by an imaginary 'light flow' coming from the past. Invisible streams pierce spacetime.

A runner on the middle of a track suddenly switches to a walk — not speeding up or slowing down, but maintaining a constant pace. Something similar may have happened to the universe itself shortly after the Big Bang.

Inflation is the rapid expansion of the newborn Universe, when quantum fluctuations were stretched to cosmic scales. The cosmic microwave background is the fossilized light of that epoch, shadows on the wall of our cosmic cave.

The explosion of a distant supernova told us something hard to believe: the universe is expanding faster and faster. The engine of this acceleration is dark energy — nearly 70% of everything that exists.

A black hole horizon is like a soap film stretched over an abyss. From a distance it looks perfectly smooth, but up close it trembles. This ripple arises from quantum fluctuations — the continuous birth and death of particles in the vacuum.

The void is never truly empty. In curved spacetime (for instance, in an expanding universe or near a black hole) the vacuum heats up. This is reminiscent of how acceleration makes particles appear seemingly out of nowhere: a phenomenon known as thermal vacuum radiation.

After the Big Bang, the universe may have been stuck in a false vacuum — a temporary state like a soap bubble ready to pop. A rare true vacuum bubble could then erupt, stretching space in the blink of an eye.

The cosmological constant is causing the universe to expand at an accelerating rate. In the far future, when all matter has dispersed, only empty de Sitter space will remain — an ideal cosmic backdrop.

Light passing near a massive body slightly changes its path — gravity pulls even on rays. In ordinary situations, a beam of light from a distant star is squeezed as if drawn together by an invisible rubber band. This property is called the null convergence condition: gravity makes light trajectories converge rather than diverge.

The Universe behaves like a soap bubble swelling in a multidimensional foam. The dark bubble model explains why it's expanding ever faster: the spacetime bubble grows, and its membrane gains a tiny thickness — about a micron, like a bacterium. At such distances, gravity 'blurs' across this thickness and weakens.

Our universe is expanding, and its future, according to cosmologists, is empty, cold de Sitter space. Understanding its quantum nature is like trying to read a book by looking only at its cover. The holographic principle suggests that all information about what happens inside a volume can be encoded on its boundary, like a picture on a film.

A translator hears not just words, but intonation, pauses, the tremor in a voice. Ordinary entropy analysis of cosmic perturbations is like meeting minutes: it records facts but loses the nuances. Pseudoentropy entropy is a new tool that captures the hidden "music" of the early universe.

Two rulers show slightly different lengths for the same table. That's roughly the situation in cosmology with the Hubble constant — the number that tells how fast the universe is expanding.

Drop a pebble into a pond, and ripples spread across the water. A black hole 'sounds' much the same when matter falls into it or when its spacetime gets a gentle jolt. These fading oscillations are called quasinormal modes, like the tolling of a bell that gradually fades away.

The universe is expanding faster and faster thanks to dark energy. But measurements of the rate give contradictory results. A new explanation: in the past, dark energy acted as a brake, slowing the galaxies' recession, and then switched to acceleration. Like a car that first rolls backward and then lunges forward.

An ordinary black hole is like a stove that heats up more as its mass shrinks. A tiny hole should glow at unimaginable temperatures and evaporate in an instant. But that scenario ignores quantum corrections — what happens when the very fabric of spacetime begins to tremble.

A taut sheet wrinkles. If you tug a corner, a smooth wave runs across; if you sharply bunch the fabric, a sharp crease forms. Space and time in Einstein's equations behave much the same way. Gravitational waves resemble the gentle ripples of the sheet, while shock fronts are like stiff folds where matter's properties change abruptly.

An ordinary lightbulb glows brighter as it heats up — everyone knows that. But a black hole the size of an atomic nucleus follows different rules.

Imagine an air mattress being stretched, with a whirlpool of water spinning on it. As you stretch, the whirlpool tightens: its size relative to the whole surface shrinks.

Drop an ice cube into boiling water, and it will melt away until nothing is left. A black hole in space behaves much the same way — except the 'boiling water' is space itself, which continuously siphons energy out of the hole.

A heavy ball rests on a trampoline, and the fabric sags beneath it. Any rolling ball nearby inevitably rolls toward the center. This is roughly how gravity works on the scale of the entire Universe. But what if the fabric were arched upward, like a dome? Then the ball would tend to roll outward.

Picture the Universe as a book with a finite number of pages. Its accelerated expansion, driven by dark energy, a mysterious substance pushing space apart, acts like an invisible binding: distant pages are forever glued together, becoming inaccessible chapters.

Stephen Hawking imagined that the universe was born not from an explosion, but by smoothly emerging from a quantum 'nothing.' In worlds with concave geometry (anti-de Sitter space), such a birth acquires a rim, like the hoop of a drum.

For a long time, dark energy, the mysterious force prodding the expansion of the Universe, was considered eternal and unchanging, like yeast that never loses its activity. But explaining such constancy through the laws of the microcosm proved impossible, and scientists began to suspect that the “leaven” might be going flat.

The quantum world does not like being pinned down to exact numbers. Physicists usually expand a complex interaction into a long series, like a sum of ever-smaller corrections.

A mathematical doughnut, a torus, sits on the boundary of a three-dimensional world where gravity acts. You can crumple and stretch it, and physicists decided to see how it behaves. Inside this world, space can be flat like a table, expanding like a soap bubble, or curved like a saddle. The doughnut boundary refused to stay smooth.

A stone falls into a pond, and ripples spread across the water. If the pond is choppy, with waves coming from all directions, the pattern gets more complicated. That's roughly how spacetime behaves around a black hole when something perturbs it: it vibrates, emitting gravitational waves.

You can picture a black hole as a whirlpool in a river: it has an edge, the event horizon, beyond which the current drags everything in irreversibly. At the center lurks the singularity, a point where the familiar laws break down.

A pencil dropped on the floor hits with its entire surface at once. But if the floor were quantum, made of countless vibrating grains of sand, the pencil would never touch a single point.

A handful of rice grains falls onto a hot skillet, and they start jumping. Each grain pushes its neighbors, and the whole pile stirs without any external hand. That's active matter: a multitude of particles that draw energy on their own and convert it into motion.

Drops from a leaky faucet beat a clear rhythm. A similar rhythm, only on the scale of the universe, has been found by astrophysicists: the formation of primordial black holes — tiny objects born in the first moments after the Big Bang — also proceeds not chaotically, but in a strictly measured way.