This page gives plain-language summaries of physics papers. We draw no link to Dost or to any other text; reading side by side is the reader's own work.
Experiment: measured. Theory: calculated or proved. Interpretation: its meaning is disputed. The labels are our own classification; a paper may have more than one nature.
Main question: Do black holes really radiate and evaporate?
In classical general relativity, a black hole is a region from which nothing can escape. Hawking, applying quantum field theory within the curvature of spacetime, showed that a black hole has a temperature like a black body and can lose mass by emitting radiation. This result has not been observed directly; it is a theoretical calculation. What is asked here is what this calculation shows and what it rests on.
On this page35. Hawking Radiation · Hawking 1974 — Black hole explosions? · 36. Bekenstein Entropy …
Hawking reported that, by looking at the behavior of quantum fields around a black hole, he found that the black hole emits thermal radiation.
The title of the paper ends with a question: 'Black hole explosions?'. It is a short Nature article and the first announcement of the result; the detailed calculation was published a year later in a separate paper.
The starting point is this: in quantum field theory, empty space is not a place where 'nothing is there'; fields exist everywhere, and the number of particles can vary with the observer. Hawking calculated which particles a distant observer would see in a spacetime in which a star collapses to form a black hole. During the collapse the modes of the field change so much that the distant observer sees particles being emitted continuously.
The result of the calculation is that the radiation resembles black-body radiation: it has a temperature proportional to the gravity at the surface of the black hole. In black holes of large mass this temperature is very low, in small black holes it is high. Since the radiation carries energy away, the black hole loses mass; as it shrinks it gets hotter, and it is expected finally to disappear.
The limits of the paper are clear: the calculation is a semiclassical approximation that treats gravity classically and the fields quantum mechanically. This approximation cannot say how the radiation continues at small masses and in the final stage. There is also no direct observation.
The article is short; the detailed theoretical calculation was later given in a separate paper. The main message in the text is that black holes are not 'black' and emit a thermal spectrum through quantum effects, which leads to mass loss. That the calculation points to an explosion-like final stage for small, primordial black holes is expressed by the question mark in the title.
This summary was written without looking at the paper's own abstract or text, relying on a known account; it should be checked against the source.
Afterwards: This result combined Bekenstein's entropy proposal with temperature and gave rise to the information-loss question (Hawking 1976).
36. Bekenstein Entropy
Main question: Does a black hole have entropy, and where does information go in a black hole?
Entropy is a measure of how many different arrangements a system can internally be in. A black hole seems to hide everything that falls into it; where does this entropy go? Bekenstein argued that a black hole should have an entropy proportional to its surface area. The question is whether the second law remains valid when black holes exist.
Bekenstein argued that the entropy of a black hole is proportional to the area of the event horizon, and that a generalized second law must include this entropy as well.
Physicists knew that black holes appear to an outside observer through three quantities (mass, rotation, charge). This means that the scattered, detailed information that enters a black hole cannot be read from outside. Bekenstein asked this question: if a hot body is thrown into a black hole and its entropy disappears, is the second law not violated?
The paper's proposal is that the black hole itself has an entropy. Its justification is Hawking's area theorem: in classical processes the horizon area of a black hole never decreases, just like entropy. Bekenstein drew a direct connection between area and entropy and said that the entropy of a black hole is proportional to the area. The total entropy is the sum of the black hole's entropy and the entropy of the matter outside, and this total does not decrease; this is the 'generalized second law.'
The paper does not give the exact value of the proportionality constant; it offers only an order-of-magnitude estimate. The exact value was obtained later with Hawking's radiation calculation. One limit of Bekenstein's argument is that, without a temperature for the black hole, it remains unclear whether this entropy is a consistent thermodynamics.
The paper is one of the first works to bring the concepts of information theory into black hole physics: entropy is read as a measure of ignorance about the internal states of a system, and the black hole's giving no detail to an outside observer is related to this ignorance. This view is also a basis for later discussions of the 'holographic principle.'
This summary was written without looking at the paper's own abstract or text, relying on a known account; it should be checked against the source.
Afterwards: Hawking's 1974 calculation gave the black hole a temperature and completed this framework; the question of where the information goes continues under the heading of the information paradox.
37. The Holographic Principle
Main question: Can all the information of a region be stored on the surface at its boundary?
Black hole entropy is proportional not to volume but to surface area. From this arose the idea that, in quantum gravity, the number of degrees of freedom in a region may be limited by the area of its boundary surface. The question is whether a three-dimensional world can be described as if encoded on a two-dimensional surface. This is a proposal of a principle, not a proven result.
't Hooft wrote an essay proposing that, for quantum gravity, the degrees of freedom should be defined on a two-dimensional surface.
't Hooft's starting point is this: the formation and evaporation of a black hole must be compatible with the principles of quantum mechanics. In quantum mechanics information is conserved and evolution is reversible.
Starting from this condition, from entropy counting and from the assumption of unitarity, the essay reaches the following conclusion: the observable degrees of freedom at the Planck scale can be described as Boolean variables defined not in three-dimensional space but on a two-dimensional lattice. That is, the information capacity of a region is determined not by volume but by the area of its boundary, and this is about one 'bit' per unit area.
The author says that this 'dimensional reduction' places heavy constraints on models of quantum gravity, that in the example of cellular automata the constraints outnumber the freedoms, and that this may be the reason a fully consistent black hole model has not been found so far. The paper is an essay: it presents no detailed model, only points to a direction.
The essay rests not on a single calculation but on several principles: the unitarity of quantum mechanics, the proportionality of black hole entropy to area, and counting arguments. For this reason the proposal is a list of constraints, not a theory.
Afterwards: This proposal took the name 'holographic principle' with Susskind's 1995 paper and found a concrete example in the AdS/CFT correspondence.
Susskind explained 't Hooft's proposal and investigated its consequences for high-energy particle collisions and string theory.
At the start of the paper, Susskind summarizes 't Hooft's idea as follows: when quantum mechanics and gravity come together, the three-dimensional world should be like an image of data stored in a two-dimensional projection; this is similar to the way a hologram works. The two-dimensional description requires only one discrete degree of freedom per Planck area, and yet must be rich enough to describe all three-dimensional phenomena.
The paper offers a preliminary, informal description of how this could be realized. One basic requirement is this: the size of particles must grow as their momenta rise far above the Planck scale. The author describes its consequences for high-energy collisions; the spreading speed of the particle runs up against the causality limit.
In the last section, string theory is treated as a possible realization: the light-front lattice string model of Klebanov and Susskind is reviewed and its similarities with the holographic description are shown. The author states openly that the agreement of the two descriptions requires unproven but plausible assumptions.
Its limit: the paper is not a complete theory but a preliminary formulation of the principle. Its realization was done later, in a separate theoretical framework.
One aspect of the paper is that it gives the first hand-drawn sketch of how information might be encoded on the boundary surface in the holographic description. The author attributes this to 't Hooft and also notes that similar ideas had long been advocated by Charles Thorn.
Afterwards: Maldacena's 1997 work gave a concrete theoretical example of the principle in a particular spacetime.
38. The AdS/CFT Correspondence
Main question: Can a theory containing gravity and a quantum field theory without gravity be two descriptions of the same thing?
Anti-de Sitter (AdS) space is a spacetime with negative curvature. The AdS/CFT proposal says that a theory of gravity inside this space may be mathematically equivalent to a conformal field theory (CFT) that lives on the boundary of the space and contains no gravity. This is a conjecture; it has been tested extensively but is not generally proven.
Maldacena proposed that the large-N limit of a certain superconformal field theory is dual to supergravity (string theory) in anti-de Sitter space.
The paper starts from the objects called 'branes' in string theory. A stack of branes is considered and the low-energy limit is taken. Two descriptions emerge: on one side a field theory living on the branes (without gravity), on the other the curved geometry around the branes.
The author shows that when the number of branes N is large, the near-horizon geometry remains reliable. This geometry is the product of anti-de Sitter space with a sphere or with other compact manifolds. On the field theory side, the superconformal symmetries correspond to the enhanced symmetries of this geometry. The four-dimensional N=4 super Yang–Mills theory in the 't Hooft limit contains IIB strings.
From this the paper's proposal follows: the compactification of M/string theory on AdS space is dual to the corresponding conformal field theory. This also means a new proposal for a definition of M theory.
Its limits: the proposal is a conjecture. Since AdS has negative curvature, the correspondence does not apply directly to our universe, and what it would mean for the real universe is not addressed in this paper.
The strength of the proposal is that the two sides complement each other in terms of computability: quantities that are hard to compute in the strongly interacting field theory can be computed more easily on the gravity side. For this reason the paper is regarded as the beginning of a program of creating a two-way dictionary.
Afterwards: After the paper, many tests of the correspondence were made; the detail is not a general proof but a large number of consistency checks. It became the most studied example of the holographic principle.