energy momentum tensor

Surf doesn't roll onto the shore as an even front. It comes in tongues of foam that merge and split apart. Magnetic fields inside materials behave much the same way: they breathe in waves, and until now nobody had seen them whole.

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.

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 scale that weighs not a body, but the very space around it. That's how Einstein's equations work in general relativity: they link the curvature of spacetime to what resides within it.

In the quiet of the quantum world, there is no emptiness. Particles are intertwined by invisible threads — entanglement. The authors of the work proposed that the very fabric of spacetime is woven from these threads. This is not just a metaphor: they built a mathematical framework where the distance between points is determined by how much shared information they hold.

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.

At the dawn of time, the universe experienced a brief moment of frantic expansion — inflation. Tiny quantum jitters of spacetime stretched to cosmic scales. These jitters, primordial fluctuations, became the seeds from which galaxies and stars later grew.

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.

In 1956, two radio telescopes at Jodrell Bank stared at Sirius, capturing not an image but the trembling of intensity.

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.

A quantum wave is like a long-exposure photograph: everything’s blurred, but the blur itself reveals motion. Usually these frozen waves are treated as convenient abstractions. Yet if at each point in the image you estimate, by brightness, the moment on the particle’s internal clock it landed there, flat space suddenly acquires curves.

An object cannot be a point. At least, not in Einstein's gravity. The equations of general relativity require that the source of the field, matter, be smeared out in space, not concentrated in an infinitesimal volume. Otherwise, infinities appear in the formulas, and a smooth spacetime cannot be constructed.

When massive bodies accelerate (say, two stars orbiting each other) the space around them doesn't stay calm. It trembles like the surface of a pond after a stone is thrown. These tremors are called gravitational waves. They carry energy away, and the source gradually loses mass.

Right after the Big Bang, space was a hot plasma — a mix of charged particles and light. In such a medium, electric currents couldn't flow on their own: a 'potential difference' was needed to push electrons relative to photons.

A supermassive black hole drifts through a cloud of dark matter. In the usual picture, this invisible substance just adds mass and barely interacts with ordinary matter. But dark matter particles could have intrinsic rotation — spin.

Pulsars are dead stars spinning with flawless rhythm. Their radio blips are more precise than atomic clocks. However, gravitational waves — ripples in the fabric of spacetime, predicted by Einstein — disrupt that rhythm.

Spacetime is like a giant sheet of paper. Fold it, and distant corners come together. Poke a pencil through, and you get a wormhole, a short tunnel through the folds. But the paper wants to spring back flat, snapping the passage shut. To keep it open, you need a rare “gasket”—matter with negative energy.

Gravity isn’t fundamental: it’s a shadow cast by entropy, the measure of disorder. Back in the 1970s, Jacob Bekenstein and Stephen Hawking found that black holes store disorder on their surface, as if information is smeared across the shell.

Gravity is the curvature of spacetime, not just an attraction, as Einstein showed. On such a curved "dance floor", even the hypothetical carriers of gravity — gravitons — move oddly.

Two electrically charged spheres attract each other with a certain force. If you replace their charges with magnetic poles, a spring scale shows exactly the same force. Black holes, it turns out, behave the same way — except instead of springs, the fabric of spacetime itself does the work.

A hot coffee on the table cools down: heat spreads from the hot center to the edges. The authors suggest that the universe behaves in a similar way, just on scales of billions of light-years. Their model describes not the usual dark energy, but a smooth redistribution of energy within the cosmos, akin to the slow flow of heat from denser regions to rarefied ones.

A juggler tosses clubs while sitting on a spinning chair. If he starts spinning the clubs all in one direction, the chair will rotate the opposite way — otherwise, the conservation of angular momentum would be violated.

Spacetime resembles a giant crystal. Gravitational waves, born from collisions of black holes, not only make it tremble — they leave indelible defects: edge ones, as if an extra plane of atoms was inserted into the crystal, and screw ones, where the layers twist.

The void is not as empty as it seems. In the quantum world, even in a perfect vacuum, pairs of particles constantly pop in and out of existence, like ripples on a pond's surface, invisible to the eye but measurable. If you place a thin partition in this ripple, it alters the wave pattern.

A broken guitar string doesn't just go silent. It still vibrates for a while, and by the character of that vibration, a luthier can tell what kind of string it was — thick or thin, tightly wound or loose. In much the same way, physicists listen to the "vibration" of quantum systems when they want to understand their structure.

Astronomers, including Vera Rubin, noticed that stars on the outskirts of galaxies rotate faster than visible mass allows. To explain this, they invented dark matter — an invisible ballast. But there's another possibility: gravity isn't always the same.