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Black holes are the most amazing celestial bodies predicted by general relativity. In classical physics, relativity determines that no matter that enters a black hole can escape from it. Its gravity is so strong that even light cannot escape its attraction.

However, in the 1970s, some physicists discovered that black holes are not completely dark and static. They found that black holes have thermodynamic properties such as entropy, temperature and radiation, and established a set of theories called black hole thermodynamics.

Black hole entropy and the second law of thermodynamics

In 1972, Israeli physicist Jacob Beckenstein put forward a bold hypothesis: black holes have entropy and are proportional to the area of their event horizon. His inspiration came from a simple and profound thought experiment: if an object with entropy (that is, information) is thrown into a black hole, then the total entropy seen by outside observers will be reduced, which seems to violate the second law of thermodynamics. To solve this paradox, Beckenstein proposed the possibility that a black hole itself has entropy, and when an object falls in, it adds enough entropy to compensate for the loss seen by outside observers.

According to general relativity, a rotating black hole without charge is described by only two parameters: its mass and angular momentum. These two parameters are completely determined by the area of the event horizon. Therefore, Beckenstein speculates that the area of the event horizon of a black hole is its most basic and common feature, which is proportional to its entropy. Specifically, he gave the following formula:

Where S{ BH} is the entropy of the black hole, k is the Boltzmann constant, c is the speed of light, An is the area of the event horizon, G is the gravitational constant and ℏis the reduced Planck constant. This formula shows two important facts: one is that the entropy of the black hole is proportional to the area of its event horizon, and the other is that the amount of information contained in the unit area of the black hole is inversely proportional to the square of Planck length.

Black hole temperature

In 1974, Stephen Hawking, a famous physicist working at the University of Cambridge in England, discovered an amazing result through the quantum field theory of curved space-time: black holes radiate particles outward. This kind of radiation is called Hawking radiation and has the following characteristics: the temperature of the black hole is inversely proportional to its mass; Hawking radiation is a quantum phenomenon which has nothing to do with the classical properties of the black hole; Hawking radiation is a kind of thermal radiation with blackbody spectrum; Hawking radiation will cause the black hole to lose mass and energy and eventually evaporate.

The mechanism of Hawking radiation can be understood by the following simplified model: in the virtual space near the black hole, particle pairs (such as electrons and positrons) are constantly generated and annihilated from quantum fluctuations. If one particle falls into the black hole and the other escapes from the black hole, outside observers will see that the escaped particle appears to have emitted from the black hole. In order to maintain the conservation of energy, particles falling into a black hole must take away some negative energy, thus reducing the mass of the black hole.

The temperature of Hawking radiation can be expressed by the following formula: where T _ {BH} is the temperature of the black hole and M is the mass of the black hole.

The first law of thermodynamics of black hole

Beckenstein and Hawking's student Simar independently discovered the relationship between the parameters of the black hole, which is the famous Beckenstein-Simar formula: where dM is the black hole mass change, dA is the event horizon area change, Ω is the angular velocity, dJ is the angular momentum change, V is the potential difference, dQ is the charge change. This relationship is similar to the first law of thermodynamics of rotating objects: so it is also called the first law of thermodynamics of black holes.

This article comes from the official account of Wechat: Vientiane experience (ID:UR4351), author: Eugene Wang

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