Question: What was Bekenstein's proposal concerning black holes?
About the article "Black hole", section "Entropy and thermodynamics".

Candidate passages:
In 1972, Bekenstein was the first to suggest that black holes should have a well-defined entropy.
Bekenstein also formulated the generalized second law of thermodynamics, black hole thermodynamics, for systems including black holes.
Both contributions were affirmed when Stephen Hawking proposed the existence of Hawking radiation two years later.
Hawking had initially opposed Bekenstein's idea.
Based on his black-hole thermodynamics work, Bekenstein also demonstrated the Bekenstein bound: there is a maximum to the amount of information that can potentially be stored in a given finite region of space which has a finite amount of energy (which is similar to the holographic principle).
In 1982, Bekenstein was the first person to develop a rigorous framework to generalize the laws of electromagnetism to handle inconstant physical constants.
His framework replaces the fine structure constant by a scalar field.
However, this framework for changing constants did not incorporate gravity.
In 2004, Bekenstein greatly boosted Mordehai Milgrom’s theory of Modified Newtonian Dynamics (MOND) by developing a relativistic version.
It is known as TeVeS for Tensor/Vector/Scalar and it introduces three different fields in space time to replace the one gravitational field. 
Later life and career.1966–1975.
The first years of marriage were hectic: Jane lived in London during the week as she completed her degree and they travelled to the United States several times for conferences and physics-related visits.
The couple had difficulty finding housing that was within Hawking's walking distance to the Department of Applied Mathematics and Theoretical Physics (DAMTP).
Jane began a Ph.D. program, and a son, Robert, was born in May 1967.
In his work, and in collaboration with Penrose, Hawking extended the singularity theorem concepts first explored in his doctoral thesis.
This included not only the existence of singularities but also the theory that the universe might have started as a singularity.
Their joint essay was the runner-up in the 1968 Gravity Research Foundation competition.
In 1970 they published a proof that if the universe obeys the general theory of relativity and fits any of the models of physical cosmology developed by Alexander Friedmann, then it must have begun as a singularity.
During the late 1960s, Hawking's physical abilities declined once more: he began to use crutches and ceased lecturing regularly.
As he slowly lost the ability to write, he developed compensatory visual methods, including seeing equations in terms of geometry.
The physicist Werner Israel later compared the achievements to Mozart composing an entire symphony in his head.
Hawking was, however, fiercely independent and unwilling to accept help or make concessions for his disabilities.
He preferred to be regarded as "a scientist first, popular science writer second, and, in all the ways that matter, a normal human being with the same desires, drives, dreams, and ambitions as the next person."
Jane Hawking later noted that "Some people would call it determination, some obstinacy.
I've called it both at one time or another."
He required much persuasion to accept the use of a wheelchair at the end of the 1960s, but ultimately became notorious for the wildness of his wheelchair driving.
Hawking was a popular and witty colleague, but his illness as well as his reputation for brashness and intelligence distanced him from some.
In 1969, Hawking accepted a specially created 'Fellowship for Distinction in Science' to remain at Caius.
A daughter, Lucy, was born in 1970.
Soon after Hawking discovered what became known as the second law of black hole dynamics, that the event horizon of a black hole can never get smaller.
With James M. Bardeen and Brandon Carter, he proposed the four laws of black hole mechanics, drawing an analogy with thermodynamics.
To Hawking's irritation, Jacob Bekenstein, a graduate student of John Wheeler, went further—and ultimately correctly—applying thermodynamic concepts literally.
In the early 1970s, Hawking's work with Carter, Werner Israel and David C. Robinson strongly supported Wheeler's no-hair theorem that no matter what the original material from which a black hole is created, it can be completely described by the properties of mass, electrical charge and rotation.
His essay titled "Black Holes" won the Gravity Research Foundation Award in January 1971.
Hawking's first book "The Large Scale Structure of Space-Time" written with George Ellis was published in 1973.
Beginning in 1973, Hawking moved into the study of quantum gravity and quantum mechanics.
His work in this area was spurred by a visit to Moscow and discussions with Yakov Borisovich Zel'dovich and Alexei Starobinsky, whose work showed that according to the uncertainty principle, rotating black holes emit particles.
To Hawking's annoyance, his much-checked calculations produced findings that contradicted his second law, which claimed black holes could never get smaller, and supported Bekenstein's reasoning about their entropy.
His results, which Hawking presented from 1974, showed that black holes emit radiation, known today as Hawking radiation, which may continue until they exhaust their energy and evaporate.
Initially, Hawking radiation was controversial.
However by the late 1970s and following the publication of further research, the discovery was widely accepted as a significant breakthrough in theoretical physics.
In March 1974, a few weeks after the announcement of Hawking radiation, Hawking was invested as a Fellow of the Royal Society, one of the youngest scientists to be so honoured.
Hawking rarely discussed his illness and physical challenges, even—in a precedent set during their courtship—with Jane.
Hawking's disabilities meant that the responsibilities of home and family rested firmly on his wife's increasingly overwhelmed shoulders, leaving him more time to think about physics.
When in 1974 Hawking was appointed to the Sherman Fairchild Distinguished Scholar visiting professorship at the California Institute of Technology (Caltech), Jane proposed that a graduate or post-doctoral student live with them and help with his care.
Hawking accepted, and Bernard Carr travelled to California with them as the first of many students who fulfilled this role.
The family spent a generally happy and stimulating year in Pasadena.
Hawking worked with his friend on the faculty, Kip Thorne, and engaged him in a scientific wager about whether the dark star Cygnus X-1 was a black hole.
The wager was a surprising "insurance policy" against the proposition that black holes did not exist.
Hawking acknowledged that he had lost the bet in 1990, which was the first of several that he was to make with Thorne and others.
Hawking has maintained ties to Caltech, spending a month there almost every year since this first visit. 
The only way to satisfy the second law of thermodynamics is to admit that black holes have entropy.
If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole.
The increase of the entropy of the black hole more than compensates for the decrease of the entropy carried by the object that was swallowed.
Starting from theorems proved by Stephen Hawking, Jacob Bekenstein conjectured that the black hole entropy was proportional to the area of its event horizon divided by the Planck area.
Bekenstein suggested formula_1 as the constant of proportionality, asserting that if the constant was not exactly this, it must be very close to it.
The next year, Hawking showed that black holes emit thermal Hawking radiation corresponding to a certain temperature (Hawking temperature).
Using the thermodynamic relationship between energy, temperature and entropy, Hawking was able to confirm Bekenstein's conjecture and fix the constant of proportionality at formula_2: formula_3 where formula_4 is the area of the event horizon, calculated at formula_5, formula_6 is Boltzmann's constant, and formula_7 is the Planck length.
This is often referred to as the Bekenstein–Hawking formula.
The subscript BH either stands for "black hole" or "Bekenstein-Hawking".
The black hole entropy is proportional to the area of its event horizon formula_4.
The fact that the black hole entropy is also the maximal entropy that can be obtained by the Bekenstein bound (wherein the Bekenstein bound becomes an equality) was the main observation that led to the holographic principle.
Although Hawking's calculations gave further thermodynamic evidence for black hole entropy, until 1995 no one was able to make a controlled calculation of black hole entropy based on statistical mechanics, which associates entropy with a large number of microstates.
In fact, so called "no hair" theorems appeared to suggest that black holes could have only a single microstate.
The situation changed in 1995 when Andrew Strominger and Cumrun Vafa calculated the right Bekenstein-Hawking entropy of a supersymmetric black hole in string theory, using methods based on D-branes and string duality.
Their calculation was followed by many similar computations of entropy of large classes of other extremal and near-extremal black holes, and the result always agreed with the Bekenstein-Hawking formula.
However, for Schwarzschild black hole, viewed as the most far from the extremal black hole, the relationship between micro and macro-state is expected to be clarified from the string theoretical viewpoint.
Various studies are in progress, but has not been elucidated.
In Loop quantum gravity (LQG) it is possible to associate a geometrical interpretation to the microstates: these are the quantum geometries of the horizon.
LQG offers a geometric explanation of the finiteness of the entropy and of the proportionality of the area of the horizon.
It is possible to derive, from the covariant formulation of full quantum theory (Spinfoam) the correct relation between energy and area (1st law), the Unruh temperature and the distribution that yields Hawking entropy.
The calculation makes use of the notion of dynamical horizon and is done for non-extremal black holes.
There seems to be also discussed the calculation of Beckenstein-Hawking entropy from the point of view of LQG. 
In addition to its ability to account for the flat rotation curves of galaxies (which is what MoND was originally designed to address), TeVeS is claimed to be consistent with a range of other phenomena, such as gravitational lensing and cosmological observations.
However, Seifert shows that with Bekenstein's proposed parameters, a TeVeS star is highly unstable, on the scale of approximately 106 seconds (two weeks).
The ability of the theory to simultaneously account for galactic dynamics and lensing is also challenged.
A possible resolution may be in the form of massive (around 2eV) neutrinos.
A study in August 2006 reported an observation of a pair of colliding galaxy clusters, the Bullet Cluster, whose behavior, it was reported, was not compatible with any current modified gravity theories.
A quantity formula_45 probing General Relativity (GR) on large scales (a hundred billion times the size of the solar system) for the first time has been measured with data from the Sloan Digital Sky Survey to be formula_46 (~16%) consistent with GR, GR plus Lambda CDM and the extended form of GR known as formula_47 theory, but ruling out a particular TeVeS model predicting formula_48.
This estimate should improve to ~1% with the next generation of sky surveys and may put tighter constraints on the parameter space of all modified gravity theories. 
The Black Holes and Revelations Tour was a worldwide concert tour by English alternative rock band Muse in support of their fourth studio album "Black Holes and Revelations".
Lasting at over 2 years, this was the band's longest tour to date.