newtonian limit

At the center of a neutron star, matter is compressed so tightly that a teaspoon weighs a billion tons. You'd think there's no better place to look for signs of quantum gravity. But between the laboratory and the fundamental scale lies a chasm of 10⁸⁰ in density. Three doors lead into this room.

As planets orbit the Sun, they don't just follow their paths: they give each other a slight tug. It's like a dance where each partner feels the movements of the others. Scientists set out to determine how strongly this mutual attraction alters the planets' trajectories. It turns out there are small corrections that were previously overlooked.

A thrown stone arcs through the air, but a planet around the Sun follows a closed curve. Why an ellipse, and not a circle or a spiral? Kepler's first law provides the answer, but its usual proof requires heavy computation. This work offers a shorter path — through a single simple ratio of velocities.

A superconductor pushes out a magnetic field like a sponge squeezing out water. This Meissner effect has been known for nearly a century, but it's usually calculated in a flat world — without gravity. In the strong field of a black hole or at enormous speeds, the picture changes.

An ordinary mirror swaps left and right. Many laws of physics don't notice the swap: they are mirror-symmetric. But some phenomena, like the weak interaction, break this symmetry. Until now, it was thought that gravity and light each break mirror symmetry in their own independent way.

A spotlight beam fades into the darkness, but if you trace it backward, you hit the lamp. The history of the universe might be the same: tracing its expansion backward, we run into a beginning. Physicists took the simplest model — a universe that stretches equally in all directions, like a cube with all sides growing.

In the first instants after the Big Bang, the universe expanded faster than light could cross it. Like an inflating balloon, but instead of rubber, it was space itself. On this balloon, ripples inevitably formed — tiny compressions and rarefactions from which all galaxies and stars later grew.

Newton gave us a world where bodies move in a void and clocks tick the same for everyone. For three centuries, this picture worked flawlessly. But it relies on many invisible props: absolute position, the 'up-down' direction, and a single rhythm of time for the entire universe. We have never measured these directly — only through the relations between objects.

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 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.

The quantum world is like a kitchen where particles suddenly appear out of "nothing." But you need a chef — a classical field acting as an external source. Glauber's theorem, long known in optics, has now been generalized: it shows exactly how the field "cooks up" particles, be they photons or gravitons.

In 2017, detectors picked up a gravitational wave from the collision of two neutron stars. Just 1.7 seconds later, telescopes saw a flash of gamma-ray burst from the same spot. That tiny delay became a treasure for physicists.

A pendulum in a noisy room is constantly jostled by people passing by. Its motion is a mix of regular swings and random jerks. Something similar happens with weak gravitational waves against the backdrop of an expanding universe. In Einstein's general relativity, these waves are tiny ripples in spacetime.

In 1998, physicists caught neutrinos doing something astonishing: the particle changes its type on the fly. That is only possible if it has mass. This became the only laboratory proof of physics beyond the Standard Model. But exactly how much a neutrino weighs remains a mystery.

A thrown stone sends ripples across water. A gravitational wave is the same kind of ripple, but in spacetime. It is produced, for example, by the merger of two black holes. In classical physics, this ripple is eternal: once created, it travels through the Universe without fading.

At the center of attention is a monopole, a special clump of a non-Abelian field (a field where the order of operations changes the result), resembling a magnetic charge without a pair. In this work, it is placed in curved spacetime described by Einstein's equations with a Gauss-Bonnet addition (a correction important at small distances).

Hot tea cools down, a pendulum comes to rest — nature loves equilibrium. But a charged black hole can reach a special, extreme state: the mass becomes minimal, and the temperature drops to zero.

General relativity, which describes the structure of the universe, does not forbid closed timelike curves. But Stephen Hawking put forward the 'chronology protection' conjecture: quantum effects should destroy such curves, making time travel to the past impossible.

Usually, a black hole is described as a frozen frame: there's mass, there's charge, and it's all static. But real objects live in time. They radiate, lose energy, and change.

A quantum particle can be a wave, and pass through two paths at once. But if something 'peeks' at which path it took, the wave disappears. This effect is called loss of interference. Usually, photons or air molecules do the peeking.

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 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.

Spring scales in a shop show weight simply: the load presses on a spring, it compresses, and the needle moves along the scale. The relation between force and compression is direct, like Hooke's law. Now imagine a scale with a tricky platform: the force is transmitted through levers, and the reading depends not only on the weight but also on how the platform itself bends.

Gravity in our world is curved spacetime. That's how Einstein's general theory of relativity describes it. But what happens to gravity at the level of atoms and particles, where quantum mechanics rules? This question has remained unanswered for nearly a century.

A translator gets distracted by every rustle in the hall, and a one-hour meeting stretches into two. That's roughly how thermal noise disrupts quantum teleportation: the carrier particles lose synchronization, and the message gets corrupted.

The first three minutes after the birth of the world are a cosmic kitchen where nature cooked the lightest atomic nuclei. The recipe is set by gravity: it controls the cooling rate of the hot 'broth' of particles. If gravity worked differently than we are used to, the dish would have turned out different — with different amounts of helium and deuterium.

Gravity isn't just the force that keeps us on the floor. On cosmic scales, it conducts galaxies, bends light rays, and decides the fate of everything. A century ago, Einstein described it as the curvature of space and time.

A stable system behaves like a ball in a bowl: give it a push, and it rolls back to the bottom. The spread of possible trajectories, uncertainty, shrinks over time. But the speed depends on the slope of the bowl's walls. In complex systems, this 'bowl' has sections of varying steepness.

At the center of the Milky Way, shrouded in dust and glare, lurks a supermassive black hole — Sagittarius A*. Around it, like moths around a flame, swarm dozens of guide stars. Two of them, S2 and S38, with eccentric orbits and periods of just a few years, have become the protagonists in testing the fundamental laws of the cosmos.

A black hole usually hides its singularity behind an event horizon — an invisible boundary from which not even light can escape. But sometimes this 'cloak' is absent, and the singularity, a point where familiar physics breaks down, is exposed to an outside observer.

In 2021, the LHAASO observatory registered gamma quanta with energies above a petaelectronvolt from sources like the Crab Nebula — a supernova remnant with a pulsating neutron star at its heart.

It all starts with a tiny scar — a thin tunnel connecting two universes. In quantum cosmology, there has long been discussion that our closed universe could have been born from "nothing" via tunneling (a process where a system overcomes a barrier that is insurmountable by ordinary standards).

Photographing hummingbird wings with an ordinary camera gives a blurry smudge. For a sharp picture, you take many rapid shots from different angles and piece them together: that's how a quantum 'snapshot' is made. In the lab, scientists 'feel' the vibrations of a tiny mirror with a laser beam.

Every river has an estuary — the place where its waters meet the sea. Spacetime, too, has its own 'shore': it is called future infinity, and it lies where all signals, light, and gravitational waves ultimately go.

In cricket, there's a special delivery — the googly. The ball spins in a way that deceives the batsman. Physics had its own googly: for nearly half a century, mathematicians couldn't make twistor theory work with real gravity. It described 'nice' fields perfectly, where everything twists in one direction. But as soon as an 'awkward' component appeared, the machinery broke down.

An endless ocean where every wave carries information about what happens in the depths. That is roughly how our Universe works under the holographic principle: the physics inside a volume can be described by processes on its boundary.

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.

In the ocean, a whirlpool pulls everything into a closed loop, just as a gravitational wave in empty space twists time into a loop. Gravitational wave — a ripple in the fabric of spacetime, and its special shape can turn the usual flow of events into a closed cycle. In such a zone, an object can return to its own past without violating the laws of physics.

According to Einstein's general theory of relativity Albert Einstein, a massive rotating body drags the fabric of spacetime along with it, much like a spoon twirled in a jar sets thick honey flowing.

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.