quantum corrections

A boiling kettle on the stove eventually boils dry — and so, according to the classical picture, a black hole should gradually vanish in a hiss of radiation. But what if you add a special ingredient to the kettle?

When you blow up a balloon too quickly, its surface starts to quiver. Something similar happened to space in the first moments after the Big Bang: the universe expanded rapidly, and the very fabric of space began to ripple.

In the quantum world, a fact becomes objective when its value is imprinted on many independent fragments of the environment, like a notice posted on hundreds of bulletin boards across the city. Each copy alone adds no new information, but it changes the rules of the game for anyone trying to erase that information.

Quantum field theory is the language physicists use to describe elementary particles and their interactions. The authors of the work decided to slightly "tweak" this language: they introduced deformations, that is, small changes to the rules of the game.

A black hole is not an eternal vacuum cleaner. It slowly loses mass by emitting particles, much like a heated stone cooling as it radiates heat. This process, discovered by Stephen Hawking, is barely noticeable for large holes, but for tiny ones, with masses comparable to a mountain, it becomes a violent evaporation.

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 that swallows matter might not just evaporate over billions of years: it could pop like a soap bubble and turn into its opposite: a white hole. This scenario emerged from numerical experiments in semiclassical gravity.

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 Josephson junction is a bridge made of superconductor, separated by an ultra-thin insulating layer. Current flows through it even without voltage. But when the current becomes too large, the bridge starts to oscillate, and even steps, Shapiro steps, appear on the voltage graph. Between these steps hide invisible gaps where the system behaves strangely.

A black hole devours everything, even light. Yet it obeys the laws of physics: it possesses entropy — a measure of the hidden information an object 'remembers.' In the 1970s, Jacob Bekenstein and Stephen Hawking discovered a strange pattern: a black hole's entropy grows not with its volume, but…

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.

In a two-dimensional universe, a black hole looks like a funnel in spacetime. But the authors of the new work went further: they proposed that the space where particle momenta 'live' is also curved, like a saddle.

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.

The early universe grew at a terrifying speed — inflating to gigantic proportions in a tiny fraction of a second. Physicists describe this burst with a single number: the exponent in a formula that resembles the steepness of a hill. The steeper the hill, the faster the ball rolls down: that is, the more rapidly space expanded.

A black hole sitting on a thin cosmic membrane (brane) resembles a heavy ball stretching an elastic sheet. In classical physics, it is bald — only mass, charge, and rotation. But add a scalar field (an invisible substance like temperature), and the hole can spontaneously grow 'fur' from this field.

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 black hole is not eternal. Even in a perfect vacuum, it slowly loses energy — a process known as Hawking radiation. Quantum effects near the event horizon create pairs of particles, one of which escapes, carrying away some of the black hole's mass.

Gravity is the invisible glue that holds stars and planets together. But what if this glue has a tiny mass? In massive gravity, the carrier particles (called gravitons) weigh a minuscule but nonzero amount. This changes the rules near black holes. The authors of the new study built on a mathematical tool — eigenvalue decomposition.

A black hole is not just an abyss where everything falls. Right at its horizon, in the so-called quantum atmosphere, a faint glow is born — Hawking radiation. This is not calm light but a churning stream of particles that can influence the most delicate quantum connections.

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.

A black hole merger is not a silent impact. The newborn hole quivers and decays, emitting gravitational waves — ripples in space itself. This signal is called the 'ringdown,' and it resembles the fading chime of a bell: it has a fundamental tone and several overtones.

A black hole is not just a dark spot. It rotates, drags space along with it, and can carry imprints of the quantum world. To describe such a hole, one must solve gravitational field equations.

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.

At the centers of many galaxies lurk supermassive black holes. One of them, Sagittarius A* at the heart of the Milky Way, has become a testing ground for a new idea. The authors of the work took Einsteinian gravity and added an unusual electromagnetic field to it.

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.

A classical black hole has a temperature and other thermodynamic properties. When physicists began accounting for changes in the cosmological constant, the energy of empty space, a strange coupling emerged in the equations.

In the scorching plasma of the infant Universe, right after inflation, conceived by Alan Guth, the kinetic dominance epoch reigned.

Einstein’s cosmological constant — a blunder or a boomerang insight? The universe’s acceleration caught physicists off guard: ΛCDM works, but why is the vacuum energy so absurdly tiny? Imagine an ocean heaving with quantum fluctuations, yet on the surface only a microscopic ripple.

A star contracts under its own gravity, and at some point its fate hangs on a razor-thin balance. Classical physics paints a grim picture: if the mass and the force of compression are tuned with terrifying precision, what emerges is not a black hole but a 'naked' singularity.

A black hole is not an eternal vacuum cleaner. It slowly evaporates, radiating energy, and along with it, as physicists believe, it should return the swallowed information. But when exactly does that start happening? The answer is given by the so-called Page curve — a graph that shows how much information the hole has already released and how much it still holds inside.

Space is like a sheet of paper: gravity bends it, making lines converge toward the center. But if you bend too hard, the paper tears, just as space, under monstrous curvature, doesn't collapse into a point but forms a torn edge. That edge is the quantum boundary.

A black hole is not just a cosmic vacuum cleaner. It is a region with such strong gravity that even light cannot escape it. But place it in a perfect fluid of dark matter and add a cloud of strings, thin filaments stretched across all of space, and the picture gets more complicated.

In the kitchen cupboard sits a jar of sugar. If you shake it, the grains will spread almost evenly — no need to place each one with tweezers. In much the same way, tiny black holes could have appeared in the first moments after the Big Bang. Their mass is like that of an asteroid, their size smaller than an atom.

A bonfire doesn't burn out all at once. If you glance at the flames at a random moment, all you see is a jumble of fire tongues, and you can never tell what exactly burned: a wet branch, an old magazine, or an armful of dry grass. But if you watch the fire hour after hour, rhythms emerge in its dance: a burst of heat, a lull, a change in color. These rhythms tell the story of what was thrown into the flames.

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.

A black hole is not an eternal vacuum cleaner. Left alone in the void, it slowly disappears, radiating energy like a puddle drying on asphalt. This process, predicted by Stephen Hawking, is called evaporation.

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 black hole is like a pot that slowly boils away. Its surface emits particles, a process known as Hawking radiation. The hotter the pot, the faster it empties. But what if the pot is not ordinary, but has a double bottom — capable of turning into a passage to another place?

Black holes lose mass like water from a bucket in the sun — an evaporation discovered by Stephen Hawking.

A light beam approaches a black hole not head-on, but at a glancing angle. If the angle is just right, the light neither falls in nor escapes: it starts looping around, like a figure skater circling the rim of a funnel. This narrow track is the photon ring. It acts like a lens, repeatedly reflecting the image of everything that falls into the hole.