![]() The quantum corrections of black hole entropy can be naturally achieved with the upper bound of wavelength of captured particles, which gives an extra logarithmic term of the Bekenstein–Hawking entropy. In this paper, the area entropy of a black hole is derived from the analogy between a black hole and a camera. After a particle with mass m falls into a black hole, the entropy of the black hole increases as Δ S = 8 π M m + 4 π m 2, and it depends not only on the particle m, but also on the black hole itself, which is quite similar to that of the resolution of an optical instrument. Due to the no-hair theorem, all information about the matter in the hole is missing for an outside observer except the total mass, angular momentum, and charge of the black hole. Likewise, the entropy of black holes means information about a black hole is missing. ![]() The more information gained, the less uncertainty or entropy a system has. Generally, more information implies less uncertainty, which is sometimes expressed simply in a quantitative statement: information is negative entropy. There are different methods for deriving the entropy of a black hole, while the physical origin of black hole entropy is still a puzzle.Įntropy measures the amount of uncertainty of a physical system. The area entropy of black holes was then reaffirmed, and the coefficient γ can be easily determined, S B H = k B A / 4 l p 2, where k B is the Boltzmann constant, A = 4 π r M 2 is the area of the black hole, and l p = ℏ G / c 3 is the Planck length. When quantum field theory of curved spacetime was applied to black holes, Hawking discovered that black holes can emit particles, called Hawking radiation. The simplest monotone increasing function of the area is a proportional function, i.e., S b h = γ A, where γ is a constant and A is the area of the black hole at its event horizon. The entropy of a black hole was suggested as a monotone increasing function of its area, since the area of a black hole never decreases in the classical theory. In the early 1970s, Bekenstein conjectured that black holes must have entropy or the second law of thermodynamics will be violated.
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