topological charge

Drop two stones of different shapes into a pond — the ripples will tell you which one was smooth and which was jagged. Gravitational waves work the same way: when two ultra-dense objects merge, the trembling of spacetime carries details about their inner workings.

A fussy thermometer shows different temperatures depending on who is looking at it. A black hole behaves much the same way: its thermal properties, entropy and temperature, depend on how we describe the information hidden inside.

A star circles a rotating black hole like a figure skater at the center of a rink. While it is far away and can be treated as a point, the dance remains predictable: the orbit follows clear laws, like music that is easy to glide to. But as it approaches, gravity begins to act unevenly.

An ordinary flashlight emits light whose waves oscillate in all directions at once. But pass that light through a special filter, and you get a beam that oscillates strictly in one plane: that's polarized light. When such a beam travels through biological tissue, the tissue's internal structure slightly alters the orientation of the oscillations.

After the Big Bang, the universe underwent a rapid expansion — inflation, smoothing out the cosmic microwave background and sowing the seeds of galaxies. But at the quantum level, chaotic fluctuations brewed in the inflaton field.

Why do some systems, from gene networks to air travel, preserve imprints of the past longer than others? For a long time, network science blamed topology: the number of connections, modularity, spectrum. But two networks with the same skeleton can remember and forget in completely different ways.

A black hole is not just a dark spot in the sky. It is a complex object whose properties depend on the geometry of spacetime around it.

A neat stack of atomic layers lies on a substrate. An invisible beam of terahertz light shines down on it, with a magnetic field applied from the side. After reflection, the beam's polarization rotates slightly.

An acoustic black hole is a fluid flow faster than sound, so sound waves can't escape. The boundary, the surface where the flow speed reaches the speed of sound, spawns pairs of phonons: sound quanta, one flying away, the other plunging inward.

A magnetic field can hold a star against complete collapse: that's the idea behind a new kind of black hole. Instead of the usual point of infinite density, inside there is a field that prevents space from crunching down to zero. It's like a spring: the harder you squeeze, the more it pushes back.

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 stone falls into a pond, and ripples spread across the water. Similarly, a black hole resting in the void may encounter a gravitational wave or a cloud of gas. It does not remain indifferent: its surface (the event horizon) bends slightly, like a stretched membrane under the weight of a drop.

Light usually travels straight, like a flashlight beam. But it can be twisted, like water in a funnel, creating a vortex in the beam. Such twisted light can carry more data: different vortices don't interfere with each other, just like different radio channels. The challenge was to make a source of such light small enough for a chip.

Black holes ring like colossal bells. Colliding or devouring matter, they oscillate and send ripples through the cosmos — gravitational waves. These are tremors of the very fabric of spacetime, and their tone reveals the hole's inner structure.

A black hole in anti-de Sitter space is not a void but rather a pot of boiling liquid. This liquid has two phases: small and large black holes, like steam and water. At a certain pressure, they merge at a critical point, just as water at 374 °C and 218 atmospheres loses the distinction between liquid and gas.