Abstract
In many papers in the literature, author(s) express their perplexity concerning the fact that the () black-hole ‘thermodynamical’ entropy appears to be proportional to its area and not to its volume, and would therefore seemingly be nonextensive, or, to be more precise, subextensive. To discuss this question on more clear terms, a non-Boltzmannian entropic functional noted was applied [Tsallis and Cirto, Eur. Phys. J. C 73, 2487 (2013)] to this complex system which exhibits the so-called area-law. However, some nontrivial physical points still remain open, which we revisit now. This discussion is also based on the fact that the well known Bekenstein-Hawking entropy can be expressed as being proportional to the event horizon area divided by the square of the Planck length.
Highlights
Some nontrivial physical points still remain open, which we revisit. This discussion is based on the fact that the well known Bekenstein-Hawking entropy can be expressed as being proportional to the event horizon area divided by the square of the Planck length
We frequently verify perplexity by various authors that the entropy of a black hole appears to be proportional to its area whereas it was expected to be proportional to its volume
Hawking, in the Abstract of his 1976 paper [1], he states A black hole of given mass, angular momentum, and charge can have a large number of different unobservable internal configurations which reflect the possible different initial configurations of the matter which collapsed to produce the hole
Summary
We frequently verify perplexity by various authors that the entropy of a black hole appears to be proportional to its area whereas it was expected to be proportional to its volume. If we use instead Sδ ( N ) = k [ln W ( N )]δ ∝ N if δ = 1/γ, Sδ=1/γ is thermodynamically extensive admissible What these two examples have in common is that, since W ( N ) scales, due to relevant correlations, differently from the usual simple case (namely W ( N ) ∝ μ N (μ > 1)), the use of the additive functional SBG violates thermodynamics, whereas the use of appropriate nonadditive entropic functionals (such as Sq , Sδ and others) satisfies thermodynamics. 1 2 invariance and magnificently unify mechanics and Maxwell electromagnetism
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