# Stephen Hawking’s theorem on the properties of a black hole is proved

(ORDO NEWS) — Physicists at the Massachusetts Institute of Technology have proven Stephen Hawking’s theorem, which states that the area of a black hole’s event horizon cannot decrease.

The paradox is that this statement contradicts another prediction of the famous physicist, according to which black holes evaporate over time. The research results are published in the journal Physical Review Letters. The scientific work is briefly described in a press release on Phys.org.

Scientists analyzed the results of observations of the gravitational wave GW150914, which passed through the Earth in 2015 and was recorded by the LIGO observatory.

This signal was generated by the merger of two black holes, which created a more massive black hole with the release of a huge amount of energy. If Hawking’s theorem is true, then the area of the final black hole should not be less than the sum of the areas of the two original black holes. The physicists concluded that, with 95 percent confidence, the area did not really shrink after the merger.

Hawking’s area theorem was derived in 1971. It is an analogue of the second law of thermodynamics, which states that the entropy of a system should never decrease, only increase or not change. It is assumed that black holes can behave like heat-emitting objects, if we take into account the quantum effects that occur at the very event horizon.

Hawking radiation occurs when a pair of virtual particles appears as a result of quantum fluctuations. Usually they immediately annihilate, but at the very event horizon, one of the particles can fall into a black hole, and the other can fly away, thereby generating radiation.

If we consider a black hole as an isolated system, then its entropy, which is proportional to the area of the event horizon, cannot really decrease. On a large scale, this rule is violated when radiation is also taken into account.

However, on a smaller scale, the theorem works. It is known that the area of the event horizon is smaller, the faster the black hole rotates, and theoretically the falling body can accelerate the rotation. However, scientists have shown that this acceleration is offset by the increase in the area of the event horizon, which occurs when a body falls into a black hole.

To do this, the researchers developed a model to analyze the signal up to the peak corresponding to two spiraling black holes to determine the mass and rotation of both black holes before merging. As black holes spiral closer to each other, they spin faster and faster, and the amplitude of the gravitational signal increases.

This makes it possible to determine the mass of both holes, the speed of their rotation and, accordingly, the area of their horizon. The resulting black hole also oscillates, producing gravitational waves that can be used to determine its mass and rotational speed.

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