Black holes are one of the most mysterious objects in the universe, and their internal structure has always been a puzzle for physicists. According to the general theory of relativity, when a star collapses into a black hole, its mass is compressed to an infinitely small, infinitely dense point, also known as a singularity. Singularities are where the laws of physics fail, and we cannot detect or understand their properties.
Recently, however, a legendary physicist made a bold point that he argues that the singularity is not real, but a mathematical illusion. He is Roy Cole, who in 1963 discovered the spatiotemporal solution of a rotating black hole, known as Cole's black hole. The Cole black hole is the closest to realistic black hole model because it takes into account the angular momentum of the black hole rather than the simplified Schwarzschild black hole.
In his new novel, Cole makes use of a powerful mathematical argument called the "regularity condition" to deny the existence of the singularity. The regularity condition requires that space-time be smooth within any finite region, with no infinity or singular values. Cole argues that if we can find a suitable coordinate system such that space-time satisfies the regularity condition inside the black hole, then the singularity is not physical, but mathematical. In other words, the singularity is just an illusion that appears because we have chosen the wrong coordinate system, just as the poles of the Earth appear to be singularities on some maps.
Comparison of the size of two black holes co-imaged by the Event Horizon Telescope (EHT): M87* at the center of the Messier 87 galaxy and Sagittarius A* (SGR A*) at the center of the Milky Way.To better understand Cole's view, we need to review the basic concepts and properties of black holes.
A black hole is an extreme celestial body that has a very large mass and a very small volume, causing it to have a very strong gravitational pull. The gravitational pull of black holes is so strong that even light can't escape, so we can't observe black holes directly. The boundary of a black hole is called the event horizon, and it is an invisible surface that can never be returned once any matter or radiation crosses it. The radius of the event horizon is called the "Schwarzschild radius" of the black hole, and it is proportional to the mass of the black hole. For example, the Sun's Schwarzschild radius is about 3 km, and the Earth's Schwarzschild radius is about 9 mm.
When matter collapses, it inevitably forms black holes. Roger Penrose was the first to propose the physics of space-time, which applies to all observers of all moments in space and in time.The formation of black holes is due to the evolution of stars. When a star runs out of nuclear fuel, it loses its balance and begins to collapse. If the mass of the star is large enough, then its collapse cannot be stopped by any force and eventually a black hole will form. This type of black hole is called a stellar black hole, and it has a mass of about several to dozens of times that of the Sun. Another type of black hole is a supermassive black hole, which is millions to billions of times more massive than the Sun, located at the center of galaxies, possibly due to the merger of multiple small black holes or the engulfment of large amounts of gas and stars.
According to the general theory of relativity, space-time is bent by matter and energy. The denser matter and energy are, the more space-time bends. A black hole is an extreme example of space-time bending, and its internal space-time is so distorted that all physical quantities become infinity or meaningless. This singularity of space-time is called a singularity, and it is where the laws of physics fail, and we cannot detect or understand their properties.
Roy Kerr found the exact solution to a black hole with mass and angular momentum in 1963 and revealed the internal and external event horizons and the internal and external event horizons, rather than a single event horizon with a dotted singularity.The existence of the singularity is due to the mathematical derivation of the general theory of relativity, but it is not necessarily real. Physicists have long wondered whether the singularity is physical or mathematical. A physical singularity means that it is real, while a mathematical singularity means that it is an illusion caused by our use of inappropriate mathematical tools or methods. For example, if we describe the Earth's surface in terms of the Cartesian coordinate system, then we will find that the Earth's poles are singularities because the longitude there is undefined. However, if we use a spherical coordinate system to describe the surface of the earth, then we will not have this problem, because the spherical coordinate system is more suitable for describing spherical objects. Therefore, the poles of the Earth are mathematical singularities, not physical ones.
Similarly, the singularity of a black hole may be a mathematical singularity rather than a physical singularity. That is, if we can find a more suitable coordinate system or method to describe the internal space-time of a black hole, then we will not encounter a singularity, but a smooth space-time. That's what Cole makes in his new **.
The Cole black hole is a rotating black hole that was discovered by Roy Cole in 1963. The Cole black hole is the closest to realistic black hole model because it takes into account the angular momentum of the black hole rather than the simplified Schwarzschild black hole. The event horizon of a Cole black hole is not a spherical surface, but a flat surface similar to a tire, and its size and shape depend on the mass and angular momentum of the black hole. There is also an inner horizon inside the event horizon of a Cole black hole, which is a ring-shaped surface that resembles a doughnut, and its size and shape also depend on the mass and angular momentum of the black hole. The singularity of a Cole black hole is not a point, but a ring, which is located inside.
In the vicinity of a black hole, space flows like a moving walk or a waterfall, depending on how you want to visualize it. Unlike in the non-rotating case, the event horizon** is divided into two parts, while the central singularity is stretched into a one-dimensional ring.In his new novel, Cole makes use of a powerful mathematical argument called the "regularity condition" to deny the existence of the singularity. The regularity condition requires that space-time be smooth within any finite region, with no infinity or singular values. Cole argues that if we can find a suitable coordinate system such that space-time satisfies the regularity condition inside the black hole, then the singularity is not physical, but mathematical. In other words, the singularity is just an illusion that appears because we have chosen the wrong coordinate system, just as the poles of the Earth appear to be singularities on some maps.
Cole's argument is based on a mathematical theorem called "Penrose-hawking singularity theorem". This theorem, proposed by Roger Penrose and Stephen Hawking in 1965, proves that under certain conditions, there must be a singularity in space-time. These conditions include:
Space-time satisfies the equations of general relativity.
There is a closed surface in space-time, called a "trapped surface", where all of its outgoing rays shrink inward rather than outward.
There is an energetic condition in space-time, that is, the density of matter and energy is non-negative.
The significance of this theorem is that it states that the existence of singularities is a corollary of general relativity, not a special case. It also illustrates that if we want to avoid singularities, we must abandon some of the assumptions of general relativity, or introduce some new physical mechanisms, such as quantum effects.
Orbital animation of a single test particle located outside the innermost stable orbit of a Kerr (rotating) black hole. Note that the particles have different radial ranges from the center of the black hole, depending on the orientation: whether they are aligned with the black hole's axis of rotation or perpendicular to it.Cole's argument is a challenge to this theorem, and he tries to prove that even if all the conditions of this theorem are met, there will not necessarily be a singularity in space-time. His idea was that if we could find a suitable coordinate system such that space-time would satisfy the regularity condition inside the black hole, then we could avoid singularities and just see a smooth space-time. Cole argues that such a coordinate system exists, but he does not give a specific example, but only assumes that such a coordinate system exists.
Rotating shadows of black holes (black), horizons, and energy layers (white). The amount of different a shown in the image is related to the relationship between the angular momentum of the black hole and its mass.At the heart of Cole's argument is that he argues that the singularity of space-time is due to our use of an inappropriate coordinate system, not to the nature of space-time itself. He argues that if we can find a more suitable coordinate system, then we can eliminate singularity and just see a smooth space-time. It's like if we use a spherical coordinate system to describe the surface of the Earth, we can eliminate the singularity of the Earth's poles.
The merit of Cole's argument is that it provides a possible way to solve the singularity problem of black holes without abandoning the basic assumptions of general relativity or introducing some new physical mechanisms. It also provides a new perspective on the internal structure of black holes and may reveal some new physical phenomena.
Mathematical simulations of distorted space-time near two merging neutron stars, leading to the creation of black holes. The colored bands are the peaks and troughs of gravitational waves, and as the amplitude of the wave increases, the color becomes brighter. The strongest waves, carrying the most energy, appear before and during the Merge event.The flaw of Cole's argument is that it does not give a specific coordinate system that makes space-time regular inside the black hole, but only assumes that such a coordinate system exists. This makes his argument unconvincing, because we cannot verify that his hypothesis is correct, or whether there are other obstacles that make it impossible to find such a coordinate system. In addition, his argument does not address the quantum effects inside black holes, as general relativity may no longer be applicable under extreme conditions and requires a more refined theory to describe it.
Cole's point is not the final answer, but an interesting hypothesis that deserves further exploration. We may never be able to directly observe the interior of a black hole, but we can find more clues through theory and experiments to unravel the mysteries of black holes.
One possible approach is to use gravitational waves to probe the inner structure of a black hole. Gravitational waves are fluctuations due to the distortion of space-time, and it can carry some information about space-time. When two black holes merge, they produce strong gravitational waves that may contain some information about the black hole's internal structure. If we can accurately measure and analyze these gravitational waves, we may be able to infer whether a black hole has a singularity, or if there is some new physical phenomenon.
Another possible approach is to use quantum theory to describe the internal structure of black holes. Quantum theory is a physical theory that describes the microscopic world, and it is incompatible with general relativity. When we consider the internal structure of black holes, we need to combine quantum theory and general relativity theory to form a unified theory called quantum gravitational theory. The theory of quantum gravity is a theory that physicists have been seeking to explain all physical phenomena, including the singularity of black holes. Currently, there is no complete theory of quantum gravity, but there are some candidate theories, such as string theory, toric quantum gravity theory, or black hole remediation theory. These theories all attempt to describe the internal structure of black holes in a quantum way, possibly eliminating the existence of singularities, or giving some new explanation.