Black hole thermodynamics is a field that studies the physical properties of black holes and their relationship to the laws of thermodynamics. This field relates the properties of black holes, such as entropy, temperature, mass, and surface area, to thermodynamic quantities and helps us better understand the behavior of black holes. The basic principles of black hole thermodynamics were developed in parallel with the four laws of thermodynamics:
1. The Four Fundamental Laws of Black Holes
1. The Zeroth Law of Black Holes
The surface gravitational potential (or surface gravitational force) of black holes is constant throughout the event horizon. This is similar to the zeroth law of thermodynamics; the temperature of a system in thermodynamic equilibrium is the same everywhere.
2. The First Law of Black Holes
A change in the mass of a black hole is related to a change in the surface area of the event horizon and reflects the principle of conservation of energy. The first law of black holes can be expressed as: dM=κ8πdA+ΩdJ+ΦdQdM = \frac{\kappa}{8\pi} dA + \Omega dJ + \Phi dQdM=8πκdA+ΩdJ+ΦdQ where dMdMdM is the change in the mass of the black hole, dAdAdA is the change in the surface area of the event horizon, κ\kappaκ is the surface gravitational force, Ω\OmegaΩ is the angular velocity at the event horizon, dJdJdJ is the change in angular momentum, Φ\PhiΦ is the electric potential and dQdQdQ is the change in the electric charge.
3. The Second Law of Black Holes
The entropy of black holes is proportional to the surface area of the event horizon and always increases or remains constant, never decreases. This law states that entropy must increase with time, similar to the second law of thermodynamics. The black hole entropy SSS is defined as: S=kc3A4ℏGS = \frac{k c^3 A}{4 \hbar G}S=4ℏGkc3A where AAA is the surface area of the event horizon, kkk is the Boltzmann constant, ccc is the speed of light, ℏ\hbarℏ is the reduced Planck constant, and GGG is the gravitational constant.
4. The Third Law of Black Holes
The surface gravitational force of a black hole never drops to zero, meaning that a black hole cannot reach absolute zero temperature. This law is similar to the third law of thermodynamics, which states that absolute zero temperature cannot be reached.
Hawking Radiation and the Temperature of Black Holes
In 1974, Stephen Hawking suggested that black holes are not actually "black" and that they can emit radiation due to quantum effects. This radiation is known as "Hawking radiation" and causes black holes to lose mass and eventually evaporate. Hawking radiation is related to the temperature of black holes, which is expressed as: T=ℏc38πGMkT = \frac{\hbar c^3}{8 \pi G M k}T=8πGMkℏc3 Where TTT is the temperature of the black hole and MMM is the mass of the black hole.
Abstract
Black hole thermodynamics helps us understand the behavior of these mysterious objects by studying their physical and thermodynamic properties. The entropy, temperature, and other properties of black holes are defined by drawing parallels with the four fundamental laws of thermodynamics. The theory of Hawking radiation explains how black holes emit radiation through quantum mechanical effects and how they can lose mass and evaporate over time.
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