Hawking's conjecture proposed 50 years ago has been overturned! Mathematicians have newly proved that **extreme black holes may exist**.

This contradicts the third law of black hole thermodynamics proposed by Hawking and others in 1973.

**Extreme black holes** are a very special case, referring to that the gravitational force at the surface or event horizon of the black hole is zero, and its surface does not attract anything, but if particles are pushed to the center of the black hole, they still cannot escape. And since the temperature of a black hole is proportional to the surface gravity, the absence of surface gravity means that **the black hole has no temperature** and cannot emit thermal radiation.

This also contradicts Hawking radiation theory, which proposes that black holes are not completely dark, but can slowly radiate energy in a specific way, thereby gradually losing mass and eventually may disappear.

However, Christoph Kehle from MIT and Ryan Unger from Stanford University have proved mathematically that this situation may exist.

And they also prove that **the existence of extreme black holes does not lead to the existence of naked singularities**. Nobel laureate Roger Penrose previously proposed that nature does not allow the existence of naked singularities. If it exists, it will destroy the causality of the universe, and the space area near the singularity may allow behaviors that violate the causality, resulting in that time and space become no longer ordered locally.

The evaluation of Columbia University mathematician Elena Giorgi:

This is a great example of mathematics feeding back to physics.

Most black holes in nature are rotating. When charged matter falls into a black hole, due to the conservation of angular momentum, the self-rotation speed of the black hole will increase, and at the same time the black hole itself will also carry a charge. In theory, as the black hole absorbs more and more matter, its charge and rotation speed will increase infinitely, and then extreme black holes will appear.

For extreme black holes, as long as any additional charge is added, its event horizon will disappear and leave a naked singularity. And its surface no longer attracts anything.

In 1973, Hawking, John Bardeen, and Brandon Carter proposed that extreme black holes cannot be formed.

This law states that the surface gravity of a black hole cannot drop to 0 in a finite time. The three scientists believe that any process that allows the charge or spin of a black hole to reach the limit may lead to the complete disappearance of the black hole's event horizon.

It is generally believed in the academic community that a black hole without an event horizon (that is, a naked singularity) is impossible to exist. In addition, since the temperature of a black hole is p roportional to the surface gravity, if there is no surface gravity, the black hole will not have a temperature either, so that the black hole cannot emit thermal radiation. But Hawking proposed that emitting radiation is a necessary attribute of a black hole.

In 1986, physicist Werner Israel once tried to simulate building an extreme black hole with an ordinary black hole and tried to make it spin faster and carry more charges, but the final conclusion shows that doing so cannot reduce the surface gravity of the black hole to 0 in a finite time.

Kehle and Unger were not originally studying extreme black holes. When they were thinking about **charged black holes** on how to form, they unexpectedly found that they could construct a black hole with extremely high charge, which is an important sign of extreme black holes.

They started from a **non-rotating, uncharged** black hole and simulated what might happen when it is placed in a scalar field.

They used a magnetic field pulse to impact the black hole and add charge to it. These pulses provided electromagnetic energy to the black hole and also increased the mass of the black hole. By emitting diffuse low-frequency pulses, the growth rate of the mass (M) of the black hole can be greater than the growth rate of the charge (q).

According to the classification, when |q| = M, it represents the formation of an extreme black hole; when |q| > M, it is a non-extreme black hole. If the growth rate of the mass exceeds the growth rate of the charge, it means that the black hole can transform from a sub-extreme state to an extreme state.

The paper not only proposed a new feature adhesion method, but also demonstrated how to construct the structure inside the black hole and analyzed the process of black hole formation and evolution, including gravitational collapse starting from regular initial data and the geometric structure outside the black hole, etc.

However, it should be noted that although the existence of the extreme black hole theory is proved by mathematical methods, it does not mean that extreme black holes must exist.

The example in the theory has the maximum charge, but currently humans have not observed black holes with obvious charges. Finding a fast-spinning black hole is more likely, so Kehle and Unger also want to construct a model so that the black hole can reach the limit in the spin speed.

But constructing such a model is more challenging mathematically. Currently, they have just started to study. All along, Kehle and Unger have been trying to explore the secrets of black holes by using mathematical methods. In 2023, Kehle and others such as his teacher Elena also proved through a 1000-page study that, in a mathematical sense, slowly spinning black holes are stable. This is very important for verifying the general theory of relativity, because if it is unstable in a mathematical sense, it may mean that there is a problem with the basic theory.

And the latest research published this year not only overturned the conjecture proposed by Hawking, but also provided new insights for the research in frontier fields such as general relativity, quantum mechanics, and string theory.

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This article is from WeChat public account: Quantum Bits (ID: QbitAI), author: Ming Min.

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