Black holes are some of the most mysterious objects in the universe. They have such strong gravity that nothing, not even light, can escape once it crosses the event horizon. For decades, scientists have studied black holes to understand how gravity behaves under extreme conditions.
Modern observations have made black holes even more important in physics. The Event Horizon Telescope (EHT) has produced images of the supermassive black holes M87* and Sagittarius A*. At the same time, the detection of gravitational waves by LIGO has allowed scientists to study black-hole mergers directly. These discoveries have provided strong evidence for black holes and have also raised important questions about what happens deep inside them.
One of the biggest questions concerns the singularity at the center of a classical black hole.
The Problem with Classical Black Holes
The first exact black-hole solution was developed by Karl Schwarzschild in 1916. Later, scientists found more complicated solutions that included electric charge and rotation. These include the Reissner–Nordström, Kerr and Kerr–Newman black holes.
Although these solutions are extremely important, they have a serious problem: they contain singularities.
In a Schwarzschild black hole, the singularity is located at the center, where (r=0). At this point, the curvature of spacetime becomes infinitely large. This means that the usual laws of classical General Relativity can no longer give a meaningful physical description.
This problem has encouraged physicists to look for regular black holes. These models are designed to keep the useful features of black holes while avoiding an infinite-density singularity at the center.
What Is a Regular Black Hole?
A regular black hole is a theoretical black hole in which the central region remains finite and well behaved. Instead of ending in a singularity, the geometry changes into a regular core.
Early ideas about avoiding singularities were proposed by scientists such as Gliner and Sakharov. They suggested that matter under extremely high pressure and density could behave differently from ordinary matter.
Bardeen later introduced one of the first well-known regular black-hole models. Other models followed, including the Hayward black hole and several rotating regular black-hole solutions.
Among these models, the Dymnikova black hole is particularly interesting. Proposed by physicist Irina Dymnikova, it has a Schwarzschild-like exterior but a completely different interior.
Far away from the black hole, the Dymnikova solution behaves almost like the Schwarzschild solution. Near the center, however, it approaches a de Sitter-like region. Most importantly, the central curvature remains finite.
This means that the Dymnikova black hole does not contain the usual physical singularity.
Why Are Tidal Forces Important?
To understand what happens to an object falling into a black hole, scientists can study tidal forces.
Tidal forces occur because gravity is slightly different at different points of an extended object. For example, the part of an object closer to a black hole experiences stronger gravity than the part farther away.
As a result, a falling object can be stretched in one direction and compressed in another. This effect is often described as spaghettification in the case of very strong gravitational fields.
Scientists use the geodesic deviation equation to calculate these effects. It describes how the distance between two nearby freely falling particles changes because of spacetime curvature.
Macedo, Silva and Landim use this method to study the tidal forces experienced by massive particles falling radially into a Dymnikova black hole.
Studying a Falling Particle
The researchers begin with the mathematical description of the Dymnikova black hole. They derive the equations that describe the motion of a massive particle falling directly toward the black hole.
They then construct a special reference frame that moves with the falling observer. This allows them to calculate the tidal forces experienced by the observer.
The study focuses mainly on two types of tidal forces:
Radial tidal force, acting along the direction of motion.
Angular or transverse tidal force, acting sideways relative to the direction of motion.
The behavior of these two forces provides important information about how an extended object would be stretched or compressed during its fall.
Schwarzschild Behavior Far Away
One of the interesting results is that the Dymnikova black hole behaves like an ordinary Schwarzschild black hole at large distances.
This means that an observer far away from the black hole would not see a major difference between the two solutions. The gravitational field and tidal forces follow the familiar Schwarzschild behavior.
However, the differences become much more important as the particle moves closer to the black hole and crosses the event horizon.
Inside the black hole, the regular structure of the Dymnikova solution begins to influence the motion and tidal forces strongly.
Tidal Forces Change Direction
The researchers find that both the radial and angular tidal forces can become zero at particular locations inside the black hole.
More importantly, the forces can change sign at these locations.
A change in sign means that the nature of the tidal effect changes. A force that was stretching the object can become compressive, or a compressive effect can become stretching.
The radial tidal force, in particular, can change from stretching to compression inside the event horizon. The angular tidal force also changes its behavior at a characteristic radius.
This is very different from the Schwarzschild case, where tidal forces become increasingly extreme as the central singularity is approached.
The Particle Does Not Reach the Center
Another important result concerns the actual path of a particle released from rest outside the event horizon.
In a classical Schwarzschild black hole, the particle continues inward and eventually reaches the singularity.
In the Dymnikova geometry, the situation is different.
The particle reaches a turnaround point inside the Cauchy horizon. At this location, its inward motion stops and it can turn around rather than continuing toward the center.
This is a major consequence of the regular structure of the black hole. The particle does not encounter an infinitely curved singularity.
What Happens to an Extended Object?
The researchers also study the geodesic deviation vector, which helps describe how an extended object changes shape during its fall.
They consider two different sets of starting conditions and follow the radial and angular parts of the deviation vector.
Far from the black hole, the results are similar to those for Schwarzschild spacetime. This is expected because the Dymnikova solution becomes Schwarzschild-like at large distances.
Inside the event horizon, however, the behavior changes significantly.
The radial part of the deviation vector initially grows as the object falls. It reaches a maximum inside the event horizon. Later, as the radial tidal force changes from stretching to compression, the radial separation begins to decrease.
The angular part shows a related but different pattern. Depending on the starting conditions, it may decrease steadily or first grow to a maximum before decreasing.
No Infinite Tidal Destruction
Perhaps the most important result is that the tidal effects remain finite in the Dymnikova spacetime.
In the Schwarzschild black hole, the radial tidal effect becomes infinitely large at the singularity. The corresponding component of the geodesic deviation vector also becomes divergent.
The Dymnikova black hole avoids this behavior. Because its central region is regular, the components of the deviation vector remain finite up to the turnaround point.
This means that the regular core changes the physical experience of matter falling into the black hole.
Why This Study Matters
The work by Macedo, Silva and Landim shows that regular black holes can behave almost exactly like classical black holes from far away while having a completely different interior.
Their study demonstrates that the de Sitter-like core of the Dymnikova black hole prevents tidal forces from becoming infinite. Instead, the tidal forces remain bounded and can even change from stretching to compression.
The falling particle also does not continue toward a singular center. It reaches a finite stopping or turnaround point inside the Cauchy horizon.
These results provide a clearer picture of what may happen to matter in a nonsingular black-hole spacetime.
Conclusion
The Dymnikova black hole offers an interesting alternative to the classical picture of black holes. It preserves the familiar Schwarzschild behavior at large distances but replaces the central singularity with a regular de Sitter-like core.
Macedo, Silva and Landim show that this change has important consequences for falling matter. Radial and angular tidal forces remain finite, change direction at specific locations, and influence the motion of freely falling particles. An object released from rest outside the black hole reaches a turnaround point rather than the central region.
Most importantly, the geodesic deviation remains finite instead of becoming infinite as it does near the Schwarzschild singularity.
In simple terms, the study shows that removing the singularity changes not only the mathematics of the black hole but also the physical experience of matter falling inside it. The Dymnikova model therefore provides a useful framework for exploring how gravity might behave when the extreme conditions at the center of a classical black hole are replaced by a regular core.
Reference: M. H. Macêdo, A. A. M. Silva, R. R. Landim, "Dymnikova Black Hole Tidal Forces", Arxiv, 2026. https://arxiv.org/abs/2608.12495
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