Signatures of charged rotating regular black holes: quasinormal modes, grey-body factors and shadows

For decades, the prevailing picture of a black hole in our universe has been defined by a single, terrifying flaw: a point at its very center where the laws of physics break down. In the standard models of gravity, this point, known as a singularity, is a place where density becomes infinite and space-time tears apart. While this mathematical oddity is hidden behind an event horizon, shielding the rest of the universe from its chaos, many physicists have long suspected that nature does not actually permit such infinities. They have proposed "regular" black holes, theoretical objects that possess an event horizon and the familiar pull of gravity, but replace that destructive central point with a smooth, finite core. The question that has lingered is whether these smoother versions of black holes would look or behave differently from the standard ones we expect, or if they would be indistinguishable from the classic models.

A recent study by Abhisek Barman Maji at the Indian Institute of Technology Kharagpur sets out to answer this by creating detailed simulations of two specific types of these regular black holes, now set into rotation. In the real universe, black holes almost always spin, and this rotation drags the very fabric of space around with them, creating a complex environment that static models cannot capture. The researcher constructed rotating versions of two theoretical models, known as the Ayón–Beato–García (ABG) and the Balart–Panotopoulos–Rincón (BPR) black holes, and then subjected them to a battery of tests to see how they would interact with the world around them. The goal was to determine if we could tell these smooth, regular objects apart from the standard, singular black holes using the tools of modern astronomy, such as the ripples in space-time caused by collisions or the dark silhouettes cast against the background of glowing gas.

To understand what these simulations reveal, one must first understand the tools used to probe them. When a black hole is disturbed, perhaps by a passing star or a collision with another black hole, it does not simply settle down immediately. Instead, it rings like a struck bell, emitting gravitational waves at specific frequencies that fade away over time. These are called quasinormal modes, and their pitch and how quickly they fade depend entirely on the shape and structure of the black hole. The study calculated these "ringing" frequencies for the rotating regular black holes and compared them to the standard rotating black hole with charge, known as the Kerr–Newman black hole. The results showed a striking pattern: the rotating BPR black hole behaved almost exactly like the standard Kerr–Newman model. Their ringing frequencies were so similar that, for all practical purposes, they were twins. However, the rotating ABG black hole told a different story. Its vibrations were distinct, shifting in ways that clearly set it apart from the standard model, especially when the black hole was spinning rapidly or carrying a significant electric charge.

The investigation did not stop at sound; it also looked at how these objects scatter light and energy. The researchers calculated "grey-body factors," which describe how much of a wave approaching a black hole gets swallowed versus how much bounces back. In this test, the BPR model again proved to be nearly identical to the standard Kerr–Newman black hole, absorbing and reflecting waves in the same way. The ABG model, however, acted as a stronger barrier, reflecting more energy at certain frequencies and delaying the transition to total absorption. This suggests that if we could measure how black holes scatter waves with extreme precision, we might be able to spot the unique signature of the ABG geometry. The study also examined a phenomenon called superradiance, where a spinning black hole can actually amplify incoming waves, stealing energy from its own rotation. Here too, the ABG model showed a different threshold for this amplification compared to the others, requiring a higher frequency to trigger the effect.

Perhaps the most visually compelling part of the study involved the "shadow" of the black hole. When a black hole sits in front of a bright background, it blocks the light, casting a dark silhouette that is slightly larger than the event horizon itself. This shadow is shaped by the unstable orbits of photons, the particles of light that circle the black hole before either falling in or escaping. The researchers mapped out these shadows for their rotating models and compared them to observations made by the Event Horizon Telescope, the instrument that famously captured the first image of a black hole's shadow. The simulations revealed that the shadow of the rotating BPR black hole was virtually indistinguishable from the standard Kerr–Newman shadow. The rotating ABG model, however, produced a noticeably different shape. By comparing these theoretical shadows to the actual measurements of the supermassive black holes M87* and Sgr A*, the study was able to place strict limits on how fast these regular black holes could be spinning and how much charge they could carry without contradicting what we see in the sky.

The overarching conclusion of this work is a tale of two different outcomes. It suggests that not all regular black holes are created equal when it comes to observation. One of the models tested, the BPR, is so similar to the standard rotating black hole that it would be incredibly difficult to tell them apart using current or near-future technology. They would ring the same, cast the same shadow, and scatter light in the same way. The other model, the ABG, presents a much more distinct face to the universe, with unique vibrations and a different shadow that could potentially be detected. This finding implies that the specific mathematical details used to remove the central singularity matter deeply. While the requirement that a black hole be "regular" is a powerful constraint, it does not force all such objects to look the same. Instead, the specific way the core is smoothed out leaves a fingerprint on the black hole's behavior, offering a potential path for astronomers to distinguish between different theories of gravity in the future, provided they can measure the subtle differences in how these cosmic giants vibrate and block the light behind them.