Full set of scenarios of high energy collision in the Schwarzschild background and kinematic censorship

In the vast theater of the cosmos, black holes are often imagined as cosmic vacuum cleaners, swallowing everything that comes too close. But for physicists, they are also laboratories for the most extreme conditions imaginable, where the rules of space and time bend until they nearly break. For over a decade, a specific question has captivated researchers: if two particles crash into each other near the edge of a black hole, could the impact release an infinite amount of energy? This idea, known as the Ba˜nados-Silk-West effect, suggested that under very specific conditions involving spinning black holes, the energy of a collision could grow without limit. However, our universe is filled with non-spinning black holes, the simplest kind, and for a long time, it seemed impossible for such a collision to happen there. The energy output remained strictly limited, capped at a modest value. Yet, this conclusion relied on looking only at the world outside the black hole. To understand the full picture, one must consider the complete map of spacetime that Einstein's equations provide, a map that includes not just our universe and the black hole, but also a mysterious "mirror" universe and a white hole—a region where matter and light can only emerge, never enter.

A team of researchers has now taken a comprehensive look at this complete map to see what happens when particles collide in these hidden regions. They did not just look at the familiar outside; they explored the entire geometry, including the white hole and the mirror universe, to classify every possible way particles could crash into one another. Their work reveals that while the simple black holes of our universe cannot produce infinite energy collisions on their own, the full mathematical structure of spacetime allows for scenarios where the energy output becomes unbounded. However, the story does not end with a simple "yes." The researchers found that while the energy can become arbitrarily large, it never actually reaches infinity in a physical sense. They uncovered a subtle mechanism, which they call kinematic censorship, that prevents the energy from becoming truly infinite, resolving a paradox that seemed to suggest otherwise.

The researchers began by mapping out the different zones of a black hole's spacetime. Imagine a diagram divided into four distinct regions. There is our universe, where we live, and the interior of the black hole, where time and space swap roles. Then there is a mirror universe, a mathematical twin to our own, and a white hole region, which acts as a time-reversed black hole, spewing matter out rather than swallowing it. In the standard view, we only see the outside of the black hole. But the full diagram connects all four regions through horizons, the boundaries that separate them. The team analyzed how particles move through these regions. They looked at particles falling in, particles moving out, and even a special kind of observer who stays at rest inside the black hole or white hole, a state that is impossible to maintain outside the horizon without a constant force.

They discovered that high-energy collisions can occur in several distinct scenarios. In the most common type, two particles crash head-on near a horizon. If they come from different directions, the energy of their impact grows as they get closer to the boundary. In the regions outside the black hole, this growth is limited. But inside the black hole or in the white hole region, the conditions allow the energy to grow much larger. The researchers identified eight specific types of these head-on collisions, depending on which region the particles start in and which horizon they approach. In some of these scenarios, the energy can become incredibly large, far exceeding anything we could ever create in a particle accelerator on Earth.

A particularly interesting case involves a "resting observer," a particle that is stationary inside the black hole or white hole. In the outside world, a particle cannot sit still without a rocket engine pushing it; it must fall. But inside, the flow of time is so warped that a particle can exist in a state of rest relative to the coordinates. When such a resting particle collides with a normal moving particle, the energy of the crash grows even more dramatically than in the head-on cases. The researchers found that if a resting particle collides with another particle near the center of the spacetime diagram, where the horizons meet, the energy can become unbounded. This led to a puzzling question: could the energy actually become infinite?

The answer lies in the delicate timing of these events. The researchers examined what happens when a collision occurs exactly at the point where the horizons cross, known as the bifurcation point. In one scenario, if a particle moves along the horizon and collides with another particle right at this point, the math suggests the energy would be infinite. However, the team showed that this is an illusion. In reality, particles cannot move exactly along the horizon in the way required to create this infinite result. If you try to set up the collision to happen exactly at the infinite energy point, the particles simply miss each other or collide at a slightly different spot where the energy is finite.

To understand why, the researchers looked at the problem from different angles, using different ways of measuring time and space. They found that the order in which you take the limits matters. If you first move the collision point closer and closer to the center and then try to make the particle a resting one, the energy seems to blow up to infinity. But if you first set up a resting particle and then move the collision point, the energy stays finite. These two ways of approaching the problem do not lead to the same result. This means that the "infinite energy" scenario is a mathematical artifact that cannot be realized in a physical event. The principle of kinematic censorship holds true: nature forbids an event where the energy is literally infinite.

The study also clarified the role of the white hole and the mirror universe. While these regions do not exist in our physical reality—they cannot be formed by the collapse of a star—they are essential parts of the mathematical description of a black hole. By including them, the researchers were able to see the full range of possibilities for particle collisions. They found that the white hole region is crucial for certain high-energy scenarios, particularly those involving particles that originate from the singularity and move outward. Without considering this region, the picture of what is possible near a black hole would be incomplete.

Ultimately, the paper provides a complete classification of how particles can collide in the Schwarzschild background, which describes a non-rotating black hole. It confirms that while the energy of a collision can become extremely large, approaching infinity, it never actually reaches that limit. The universe has a built-in censorship that prevents the energy from becoming truly infinite, ensuring that the laws of physics remain consistent even in the most extreme environments. This work not only settles a long-standing question about the limits of energy in black hole collisions but also offers a framework for understanding similar phenomena in more complex black holes, such as those with electric charge or inner horizons. The researchers have shown that even in the most chaotic and energetic corners of spacetime, nature maintains a strict order, preventing the impossible from happening.