logarithmic correction

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.

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.

A black hole has three laws, just like an ideal gas. The first: energy is conserved. The second: the horizon area never decreases. And the third, the most finicky, demands that at zero temperature the entropy (a measure of disorder) tend to zero or a universal constant.

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 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.

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 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.

Two charged spheres collided and flew apart in different directions. You'd think it was all over — but the light from their farewell still wanders through space. In the ordinary world, this is a well-known effect: an accelerated charge always radiates.

Cosmologists are facing a curious situation: two reliable tools draw slightly different maps of the same universe. One tool is the map of ancient light (the cosmic microwave background), and the other is the map of galaxy distribution. They broadly agree, but in details they diverge.

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.

A whirlpool gulps down water, but splashes most of it back out. That's roughly how a black hole behaves when too much matter falls onto it. In a new study, astrophysicists ran 32 computer simulations to understand how a black hole's parameters — mass, spin, and "appetite"—control these cosmic fountains.

Imagine a factory capable of producing a million parts per hour, yet it only makes a hundred. That's roughly how our Universe behaves when viewed through the lens of entropy — a measure of disorder that, according to physics, must only increase. The main "machines" of this factory are supermassive black holes.

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…

In 1973, Jacob Bekenstein proposed that black hole possess entropy — a measure of hidden disorder. Stephen Hawking later confirmed this by adding radiation, but the microscopic origin of entropy remained obscure.

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.

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.

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.

A swarm of tiny invisible particles, like a cloud of pollen, drifts through space. A black hole sits in its path. Some particles fall in and vanish forever; others swing around the trap and fly away. The physicists built a map showing exactly how much matter gets swallowed and how much survives.

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.

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 most galaxies lurk supermassive black holes — the overlords of gravity. Since 2019, thanks to interferometry with very long baselines, we’ve glimpsed their shadows: dark silhouettes set against a blazing gas backdrop. But what exactly is painting that shadow?

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.

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 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.

When a giant star runs out of fuel, it collapses into a black hole. Such a hole has an outer boundary — the event horizon, beyond which even light cannot escape. But many black holes also have an inner boundary — a second horizon that separates the outer layers from the singularity core.

A black hole is like a perfectly dark room: from outside, you can't see what's inside, and anyone crossing the threshold seems to vanish from the outside world. But what does the falling observer feel? In classical physics, nothing special: the event horizon isn't marked by any signpost.

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 black hole is not just a vacuum cleaner. It glows faintly, emitting particles — this idea was proposed by Jacob Bekenstein, who connected the hole's temperature to its degree of disorder. Detecting such radiation in space is incredibly difficult.

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.

At the center of galaxy M87, 55 million light-years away, lurks a black hole with a mass of 6.5 billion Suns. In 2019, the Event Horizon Telescope (EHT) gave us its first portrait: an orange donut with a dark core. But the donut is not the abyss itself.

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.

A cosmic ray approaches a black hole almost tangentially. Instead of falling straight in, it lingers on an unstable orbit, like an acrobat balancing on a tightrope over an abyss. After a few loops, the light finally escapes toward a distant observer. Such rays produce multiple images of the same source, known as higher-order images.