2012/12/06 by Alfonso-Faus, Antonio, Alfonso, Màrius Josep Fullana i
#FOS: Physical sciences #General Physics (physics.gen-ph)
paper · doi:10.48550/arxiv.1212.1711
Using the Bekenstein upper bound for the ratio of the entropy S of any bounded system, with energy E = Mc2 and effective size R, to its energy E i.e. S/E < 2πk R/ℏ c, we combine it with the holographic principle (HP) bound ('t Hooft and Susskind) which is S ≤ πk c3R2/ℏ G. We find that, if both bounds are identical, such bounded system is a black hole (BH). For a system that is not a BH the two upper bounds are different. The entropy of the system must obey the lowest bound. If the bounds are proportional, the result is the proportionality between the mass M of the system and its effective size R. When the constant of proportionality is 2G/c2 the system in question is a BH, and the two bounds are identical. We analyze the case for a universe. Then the universe is a BH in the sense that its mass M and its Hubble size R ≈ ct, t the age of the universe, follow the Schwarzschild relation 2GM/c2 = R. Finally, for a BH, the Hawking and Unruh temperatures are the same. Applying this to a universe they define the quantum of mass ∼ 10-66 g for our universe.