Mark Srednicki has claimed to demonstrate the entropy ~ area law -- https://arxiv.org/pdf/hep-th/9303048.pdf
Does anyone know of an independent verification or another demonstration of this result?
Is there a proof of this law?
in "Why is the black hole entropy (almost) linear in the horizon area?" (link attached) Gour & Mayo give classical thermodynamical reasons for it. Based on a gedanken experiment that describes a merge of two identical holes it is claimed that the generalized second law (GSL) would be violated had the entropy been ~log(area). Solving the inequality in eq. 19 is essentially the assumption that for arbitrary M^2 and since S_0 > 0 we must have -- (64 π)^γ - 2^(1 + 4 γ) π^γ > 0. Indeed, this restricts γ > 1/2. For γ=1 we have, S_0/ η < 32 π M^2.
We follow the same exercise with log(A) to get
S_0/η < log(64πM^2) - 2 log(16πM^2) = -log(4πM^2) = -log(A/4), which leads to A < 4 exp(-S_0/η) or M^2 < (1/4π) exp(-S_0/η). If you accept that the initial condition had 2S_0 (each for a hole) then it is convincing. But note that the final condition has only a single S_0 which may suggest double counting for the initial condition. In other words when is a system comprised of two holes disparate from the merged product? Moreover, how do we calculate and account for the entropy lost in gravitational waves -- in the LIGO event reported in February 2016, about 3 Solar masses of radiation went out of the system. The same goes for the chirp mass... (https://losc.ligo.org/events/) Is this part of the S_0, etc.
http://xxx.lanl.gov/pdf/gr-qc/0011024v2
if entropy presupposes a Close System, then all entropy laws fail; closed Systems do not exist!
Surface area of a sphere of radius equal to Schwarzschild radius Rs has a special property. It is a "boundary" which is shared by both interior and exterior of a black hole. In this basis black hole area law for entropy was formed.
When black holes are formed, matter and radiation fall into it, where both quantities carry entropy along with them. An exterior observer, to whom information does not reach from inside the black hole, may be misled in this situation, thinking that a finite portion of entropy has disappeared. Entropy laws for the black hole physics try to put a handle on this.
An argument which depends on the assumption that every qubit of information, [1,0] or [0,1] can occupy one and only one 'box' on the horizon's area goes as follows. Since the sum of the boxes must equal the area, we have, N = A, where N is the number of qubits. We calculate the number of ways by which we can arrange the qubits on the horizon, as the sum of all the possible combinations of qubit configurations, W(N) = ΣN!/[(N-k)!k!], with the sum running from k=0 to k=N. This sum is calculated to be 2N, which suggests that we could simply put it this way: each qubit has two representations, for N qubits there are therefore, 2N ways to arrange this collection of qubits. Since according to the Boltzmann principle S=log[W], we have, S=log[2N], or S ∝N = A.