In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature$\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K$ where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.

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Particle Creation by Black Holes

Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.

Quantum Cryptography

There are a number of similarities between black-hole physics and thermodynamics. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. After a brief review of the elements of the theory of information, we discuss black-hole physics from the point of view of information theory. We show that it is natural to introduce the concept of black-hole entropy as the measure of information about a black-hole interior which is inaccessible to an exterior observer. Considerations of simplicity and consistency, and dimensional arguments indicate that the black-hole entropy is equal to the ratio of the black-hole area to the square of the Planck length times a dimensionless constant of order unity. A different approach making use of the specific properties of Kerr black holes and of concepts from information theory leads to the same conclusion, and suggests a definite value for the constant. The physical content of the concept of black-hole entropy derives from the following generalized version of the second law: When common entropy goes down a black hole, the common entropy in the black-hole exterior plus the black-hole entropy never decreases. The validity of this version of the second law is supported by an argument from information theory as well as by several examples.

Black holes and entropy

were proposed in the early 1980’s [Benioff80] and shown to be at least as powerful as classical computers an important but not surprising result, since classical computers, at the deepest level, ultimately follow the laws of quantum mechanics. The description of quantum mechanical computers was formalized in the late 80’s and early 90’s [Deutsch85][BB92] [BV93] [Yao93] and they were shown to be more powerful than classical computers on various specialized problems. In early 1994, [Shor94] demonstrated that a quantum mechanical computer could efficiently solve a well-known problem for which there was no known efficient algorithm using classical computers. This is the problem of integer factorization, i.e. testing whether or not a given integer, N, is prime, in a time which is a finite power of o (logN) . ----------------------------------------------

A fast quantum mechanical algorithm for database search

The perceptual recognition of objects is conceptualized to be a process in which the image of the input is segmented at regions of deep concavity into an arrangement of simple geometric components, such as blocks, cylinders, wedges, and cones. The fundamental assumption of the proposed theory, recognition-by-components (RBC), is that a modest set of generalized-cone components, called geons (N £ 36), can be derived from contrasts of five readily detectable properties of edges in a two-dimensiona l image: curvature, collinearity, symmetry, parallelism, and cotermination. The detection of these properties is generally invariant over viewing position an$ image quality and consequently allows robust object perception when the image is projected from a novel viewpoint or is degraded. RBC thus provides a principled account of the heretofore undecided relation between the classic principles of perceptual organization and pattern recognition: The constraints toward regularization (Pragnanz) characterize not the complete object but the object's components. Representational power derives from an allowance of free combinations of the geons. A Principle of Componential Recovery can account for the major phenomena of object recognition: If an arrangement of two or three geons can be recovered from the input, objects can be quickly recognized even when they are occluded, novel, rotated in depth, or extensively degraded. The results from experiments on the perception of briefly presented pictures by human observers provide empirical support for the theory. Any single object can project an infinity of image configurations to the retina. The orientation of the object to the viewer can vary continuously, each giving rise to a different two-dimensional projection. The object can be occluded by other objects or texture fields, as when viewed behind foliage. The object need not be presented as a full-colored textured image but instead can be a simplified line drawing. Moreover, the object can even be missing some of its parts or be a novel exemplar of its particular category. But it is only with rare exceptions that an image fails to be rapidly and readily classified, either as an instance of a familiar object category or as an instance that cannot be so classified (itself a form of classification).

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Recognition-by-Components: A Theory of Human Image Understanding.

Evaluation of a marine mammal status and trends contaminants indicator for European waters.

An investigation into the effects of climate change on baleen whale distribution in the British Isles.

EXTRACT 10 – A Spinor Approach to General Relativity†

While the effects of Einstein’s general relativity are not observationally significant for the every day physics of terestial gravity, nor (in almost all cases) for the motion of planets about the sun, nor (as far as we know) for stars within galaxies, nor for galaxies about one another, the theory does give some observed (or observable) corrections to Newtonian theory in suitable circumstances. In addition to the ‘classical’ observed perihelion advance of Mercury (and, to a lesser extent of other planets as well) and the observed bending of light by the sun’s gravitational field, general relativity contributes significantly to the structure of neutron stars, to the stability of stellar models and to dynamical effects in close binary systems owing to energy loss in gravitational radiation. There are also effects which, though small in general relativity, are absent altogether in standard Newtonian theory, such as the slowing down of clocks in a gravitational potential, the time delay in light signals passing near the limb of the sun (both observed effects) and the very existence of energy-carrying gravitational waves (whose observational status is more dubious). Moreover, there are situations in which general relativity, effectively, provides a gross new effect, such as in the structure of black holes (an example of which apparently resides in the X-ray source Cygnus X-1).

Aspects of General Relativity

Much of the theoretical work that has been carried out in General Relativity, particularly in the earlier years of the subject, has been concerned with finding explicit solutions of Einstein’s field equations, either in the vacuum case or, with suitable equations of state, when matter is present. These have been very useful in giving us some sort of feeling for the nature of more general ‘ physically reasonable ’ solutions, but they can, at best, only be rough approximations to such solutions. Exact solutions must, owing to the limitations of human energy and ingenuity, and to the complexity of Einstein’s equations, involve a number of simplifying assumptions, such as special symmetries or particular algebraic forms for the metric or curvature. Sometimes it is legitimate to regard such a special solution as the first term in some perturbation expansion towards something more realistic. But in the highly nonlinear situations of strong gravitational fields, such as in gravitational collapse to a black hole, or perhaps also in cosmology, it is often not clear when the results of such perturbation calculations (themselves often very complicated) can be trusted. High-speed computers can come to our aid (Smarr 1979, this symposium), of course, and can often give important insights in particular situations. But complementary to these are the global qualitative mathematical techniques that have been introduced into relativity over the past several years (Hawking & Ellis 1973; Penrose 1972).

Roger Penrose

Papers

Evaluation of a marine mammal status and trends contaminants indicator for European waters.

An investigation into the effects of climate change on baleen whale distribution in the British Isles.

EXTRACT 10 – A Spinor Approach to General Relativity†

Aspects of General Relativity

Global General Relativity