Acceleration radiation, quasinormal modes and quasi-bound states in generic rotating regular black holes

Black holes are often imagined as cosmic vacuum cleaners, but in modern physics, they are also understood as hot, thermodynamic objects that glow with a faint, theoretical light. This glow, known as Hawking radiation, arises because the intense gravity near a black hole's edge disturbs the quantum vacuum, creating particles that escape into space. However, this picture changes dramatically when the black hole spins. A rotating black hole drags the fabric of space and time around with it, creating a region where nothing can stand still. In this environment, the rules for how particles are created and how energy flows become far more complex, depending on whether the particles are moving with the spin or against it. Scientists have long sought to understand exactly how a detector, like a tiny atom falling into such a spinning void, would perceive this radiation. Does it see a simple, uniform heat? Or does the spin and the specific shape of the black hole's interior create a more intricate signal?

A team of researchers has tackled this question by studying a specific class of theoretical black holes that avoid the infinite density, or singularity, found at their centers. These "regular" black holes are mathematical models where the core remains smooth and finite, offering a way to explore what happens when the extreme conditions of a black hole are slightly softened. The researchers focused on how a neutral, two-level atom—essentially a simple quantum system with a ground state and an excited state—would behave as it fell freely through the event horizon of these spinning, regular black holes. They wanted to know if the atom would get excited by the radiation, and if so, whether the rate of this excitation followed the standard rules of thermal heat or if it carried a unique fingerprint of the black hole's rotation and internal structure.

The study reveals that the answer is not a simple "yes" or "no" to a uniform temperature. Instead, the atom's response is a delicate balance between the black hole's spin, the atom's path, and the specific way the black hole's mass is distributed near its center. The researchers found that for an atom falling straight into the horizon, the radiation it detects is indeed related to the black hole's temperature, but this relationship is modified by the atom's motion and the precise geometry of the horizon. Crucially, they discovered that the standard assumption that all black holes of the same size and spin behave identically is not entirely true. The internal structure of these regular black holes, defined by how their mass tapers off near the center, leaves a measurable imprint on the radiation. This imprint appears as a small but distinct correction to the expected energy exchange, a correction that depends on the specific mathematical "profile" of the black hole's interior.

To get these results, the team did not rely on approximations that might miss subtle details. They performed a rigorous calculation that tracked the atom's journey from a safe distance down to the horizon, accounting for the changing speed of the atom and the twisting of space-time. They compared three different types of regular black holes, each with a slightly different internal mass distribution, and found that while they all produced radiation, the strength and character of that radiation varied. For instance, one type of regular black hole, which resembles a specific solution from nonlinear electrodynamics, produced a slightly different signal than another type that mimics a different theoretical model. The researchers also checked their work by solving the equations for the waves themselves, confirming that the signals predicted by the falling atom matched the independent behavior of the waves outside the black hole.

The study also explored what happens if the atom is not falling freely but is instead forced to move in a circle around the black hole at a fixed distance. In this scenario, the atom does not experience the same thermal glow as the falling one. Instead, its response depends heavily on whether it is orbiting in the same direction as the black hole's spin or in the opposite direction. This distinction is vital: an atom moving against the spin sees a different energy landscape than one moving with it. The researchers showed that this orbital motion creates a response that is fundamentally different from the heat-like radiation seen by a falling observer. The orbital atom does not simply see a thermal bath; it sees a complex interaction where its own speed and direction dictate whether it absorbs or emits energy, a result that challenges the idea that all observers near a black hole see the same thermal environment.

One of the most significant findings of the work is a clarification of how we should think about the energy and entropy of these rotating black holes. In standard physics, there is a simple rule linking the black hole's mass, its spin, and its surface area, much like a law of thermodynamics. However, the researchers found that for these specific regular black holes, this simple rule does not hold automatically. The internal structure of the black hole introduces extra terms that must be accounted for, meaning that the standard bookkeeping of energy and entropy requires a more careful, conditional approach. This does not mean the laws of thermodynamics are broken, but rather that applying them to these exotic objects requires a more detailed map of the black hole's interior. The study concludes that while the horizon of a spinning black hole does radiate, the exact nature of that radiation is a conversation between the geometry of space-time, the motion of the observer, and the hidden structure of the black hole's core.

The researchers also examined the stability of these black holes by looking at how waves scatter off them, a process known as quasinormal modes. These modes are like the ringing of a bell after it is struck, revealing the shape and size of the object. By calculating these frequencies for their regular black holes, they confirmed that the exterior space around these objects behaves consistently with their theoretical models. This independent check gave them confidence that their calculations of the falling atom were correct. The work serves as a precise test of how quantum mechanics and gravity interact in a rotating environment, showing that even when we remove the infinite singularity, the physics remains rich and full of surprises. It suggests that if we could ever observe a real black hole with a non-singular core, the radiation it emits would carry a signature of that core's structure, offering a potential way to distinguish between different theories of gravity.

Ultimately, this research provides a clearer picture of the "horizon-brightened" radiation that occurs when an object accelerates near a black hole's edge. It moves beyond the idea of a simple, uniform heat to show a more nuanced reality where the observer's path and the black hole's internal makeup matter. The findings suggest that the universe is more complex than a simple thermal model allows, even in the extreme environment of a black hole. By carefully separating the effects of the horizon from the effects of the detector's motion and the black hole's interior, the team has provided a more accurate map of how quantum fields behave in the presence of strong, rotating gravity. This work does not claim to have solved the mystery of black holes, but it has refined the tools we use to ask the right questions, ensuring that our understanding of these cosmic giants is built on a foundation of precise, verified details rather than broad assumptions.