schwarzschild metric

In 2015, the LIGO detectors caught the first ripple of spacetime from a black hole merger. Since then, hundreds of such events have piled up, each carrying the imprint of its ancestry: whether the holes were born together from a single pair of stars or met by chance in a dense cluster. The difference shows in the direction of their spin axes.

When two heavy balls merge into one, ripples spread across the water's surface for a long time. A black hole behaves similarly: after a merger, it 'rings' for a while, emitting special gravitational oscillations — quasinormal modes. Usually, this ring fades quickly, like an echo dying out in an empty hall.

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 dance floor where couples whirl. At the center, an invisible master of ceremonies sets the rhythm. This is the supermassive black hole at the heart of the Milky Way, and the couples are stars whose orbits astronomers have tracked for years. But what if the master himself is wrapped in a fluffy fur coat of tenuous matter?

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 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.

Somewhere in the center of a galaxy, a black hole is spinning. It doesn't hang in a void — around it swirls an invisible swarm of dark matter particles. Until now, this swarm was described for non-rotating holes, but in reality, holes always rotate.

A black hole is not just a dark sphere. In string theory, it can grow 'hair'—extra scalar fields such as the axion and the dilaton. These fields gently alter the geometry of space around the hole.

A black hole rings like a bell after being struck. This ring is the gravitational waves that detectors pick up. But what changes if the space around the hole is curved not only by its mass but also by an additional quantum correction?

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.

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.

An invisible scaffold holds galaxies together, keeping them from flying apart. This is dark matter — matter that doesn't shine and barely interacts with ordinary stuff. Astrophysicists have long debated what it's made of.

The universe isn't just a place; it's a schedule of events: what happened earlier and what happened later. In Einstein's geometry of spacetime, this schedule sometimes breaks off. For instance, inside a black hole, particle paths run into a singularity — an edge beyond which the equations stop.

Drop a stone into a calm lake, and ripples spread in even circles. Spacetime around a massive body behaves similarly: if the body is perfectly round, the disturbances it causes are symmetric. A black hole in general relativity resembles a perfectly smooth mirror of water.

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's shadow isn't just a black circle. Usually, we see a dark void surrounded by a glowing ring of hot gas. But if a black hole wasn't born from a dying star but has existed forever, its shadow might hide a surprise. An eternal black hole is a solution to Einstein's equations with no past and no collapse.

A black hole is not a vacuum cleaner. By itself, it doesn't pull everything in more strongly than an ordinary star of the same mass. But if there's a magnetic field nearby and charged particles flying around, an interesting game begins.

A black hole is like a perfect safe: everything that falls in disappears without a trace. But quantum mechanics whispers that on the microscopic level, information is not lost but recorded on an invisible "surface." Understanding this record means unraveling the fabric of gravity.

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.

You could send a short radio pulse toward a black hole and wait for the reflected echo. Intuitively, the shorter the signal, the better it would probe the finest details of spacetime right at the horizon: that region from which even light cannot return.

A black hole is like a perfectly smooth sphere. It has no features — only mass, charge, and spin. This rule is called "no-hair." But nature loves to complicate things: sometimes a cloud of a scalar field (a special field described by a single number at each point) spontaneously appears around a black hole.

A black hole is not an absolutely black bag. In 1974, Stephen Hawking showed that it glows — faintly, but continuously. This radiation is born not inside, but outside, right at the boundary from which even light cannot escape. A new study sharpens the picture.

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 black hole doesn't just spin: it's surrounded by bristles of an extra field (the Kalb–Ramond field). This paper explores how a massive field (waves with mass) behaves near such a black hole when it's almost spinning at its maximum rate. The Klein–Gordon–Fock equation for this field was separated into two independent parts — radial and angular.

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 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.

At the very heart of the Milky Way, stars whirl around an invisible supermassive black hole. One of them, S301, completes an orbit in just 8.7 years. Its path is a highly squashed ellipse: sometimes it grazes the black hole, sometimes it shoots far away. At closest approach, the distance to the black hole is tiny by cosmic standards.

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.

A black hole is not an eternal vacuum cleaner. Surround it with a non-ideal fluid (matter with internal friction), and the geometry starts to lead a life of its own. The authors of the paper showed that a special geometric flow, the almost η-Ricci–Yamabe soliton, acts like an invisible sculptor.

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.

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 campfire burns steadily and long. But when the wind blows, the flame flickers out, leaving only embers. A similar story plays out with the gravastar — a hypothetical object that was supposed to replace the black hole. An ordinary black hole hides a singularity — a point where the laws of physics break down.

A black hole's horizon is not a wall but rather a one-way membrane. Anything that crosses it disappears forever. Stephen Hawking showed that this boundary should glow faintly, emitting particles. But catching such radiation from a real black hole is impossible: it's too far and too dim. Physicists have found a workaround: build a "toy" black hole out of magnetic atoms.

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.

A pair of black holes circles in a dance, gradually drawing closer. They lose energy and spin — a process known as angular momentum radiation. In standard Einstein theory, only gravitational waves carry away angular momentum.

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.