QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

OVERVIEW The O.J. Simpson " trial of the century " in the mid-1990s captured the attention of the American populace more than any other public spectacle since the kidnaping of the Lindberg baby in the 1920s. A prominent football player and popular sportscaster was charged with a gruesome double homicide. The attorneys for the prosecution and defense were of various races and genders. The evidence presented on each side was at times amazingly simple, visual, and emotional, and at times was verbal, abstract, and probably incomprehensible to jurors. The witnesses included individuals of diverse styles, demeanors, and credibility. The jurors, the recipients of the messages from these various sources, were themselves a mixed group of people of diverse backgrounds, beliefs, and personal experiences who had to sift through the trial material and arrive at a decision as to whether the defendant had been proven guilty or not. The context in which all of this took place was at times tense and sad, and at times filled with humor and positive feelings. Not surprisingly, no experiment has ever captured the extraordinary complexity inherent in this situation, yet almost all of the variables present in this trial (and many not present) have been examined in the social psychological literature on attitude formation and change. This chapter provides an overview of research on these diverse variables and addresses the processes by which these variables are thought to result in influence. Although it has become a cliché to say that the attitude construct is the most indispensable concept in contemporary social psychology, this statement appears as true today as when Allport (1935) initially wrote it in reviews of the attitude concept). Attitudes remain important as we enter the 21st century because of the fundamental role that individuals' attitudes, both explicit and implicit (Greenwald & Banaji, 1995), play in the critical choices people make regarding their own health and security as well as those of their families, friends, and nations. From purchase decisions provoked by liking for a product to wars spurned by ethnic prejudices, attitudes help to determine a wide variety of potentially consequential outcomes. Before turning to the relevant studies, it is useful to address some definitional issues. The term attitude is used to refer to a person's overall evaluation of persons (including oneself), objects, and issues. Thus, one's attitude refers to how favorably or unfavorably or how positively or negatively in general …

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Attitude change: Multiple roles for persuasion variables.

r 9HE purpose of this paper is to explore a hypothesis, based on acIcumulating evidence, regarding the character of inventions likely to issue from the research laboratories of the large industrial corporations. Simply put, this hypothesis may be stated as follows: with few exceptions, the large industrial laboratories are likely to be minor sources of major (radically new and commercially or militarily important) inventions; rather they are likely to be major sources of essentially "improvement" inventions. Put more precisely, the hypothesis states that the proportion of all minor inventions originating in the large industrial laboratories is likely to exceed the proportion of all major inventions originating in these laboratories. Note that the stress on the relative importance of these laboratories as sources of improvement inventions is not necessarily a denigration of the economic importance of this contribution. The cumulative effect of these improvement inventions may be, and often has been, of substantial importance over long periods of time for advancing technology, investment opportunities, and economic growth. The stress on improvement inventions as the principal product of the research laboratories of the large industrial corporations is meant simply to emphasize that, whatever the importance of their contributions, most of the latter is not likely to involve radically new inventive activity. I cannot claim originality for this hypothesis. After it suggested itself in the course of my investigations, I discovered that others, some of them in the most unlikely positions,2 had earlier said much the same thing. But, apart from occasional remarks, I can find no discussions attempting to explain or justify it. And because, if reasonably accurate, it has numerous ramifications, I have felt the need to set down an extended analysis of 1 I wish to thank members of the Seminar on Law and Technology, sponsored by the University of Wisconsin Law School under the auspices of the Ford Foundation, for their many helpful comments on this paper. Especially do I wish to thank Professors Jacob Schmookler, Robert Merrill, John Stedman, Harrison White, and John Heath. 2 See particularly the statement quoted below (p. 114) of D)r. Frank Jewett, former president of Bell Laboratories.

The journal of political economy

Social dilemmas occur when the pursuit of self-interest by individuals in a group leads to less than optimal collective outcomes for everyone in the group. A critical assumption in the human sciences is that people's choices in such dilemmas are individualistic, selfish, and rational. Hence, cooperation in the support of group welfare will only occur if there are selfish incentives that convert the social dilemma into a nondilemma. In recent years, inclusive fitness theories have lent weight to such traditional views of rational selfishness on Darwinian grounds. To show that cooperation is based on selfish incentives, however, one must provide evidence that people do not cooperate without such incentives. In a series of experimental social dilemmas, subjects were instructed to make single, anonymous choices about whether or not to contribute money for a shared “bonus” that would be provided only if enough other people in the group also contributed their money. Noncontributors cited selfish reasons for their choices; contributors did not. If people are allowed to engage in discussion, they will contribute resources at high rates, frequently on irrational grounds, to promote group welfare. These findings are consistent with previous research on ingroup biasing effects that cannot be explained by “economic man” or “selfish gene” theories. An alternative explanation is that sociality was a primary factor shaping the evolution of Homo sapiens. The cognitive and affective mechanisms underlying such choices evolved under selection pressures on small groups for developing and maintaining group membership and for predicting and controlling the behavior of other group members. This sociality hypothesis organizes previously inexplicable and disparate phenomena in a Darwinian framework and makes novel predictions about human choice.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0140525X00025292

Selfishness examined: Cooperation in the absence of egoistic incentives.

Foreword A. Rapoport. Acknowledgments to the second edition. Acknowledgments to the first edition. Preface to the second ediction. Introductory Chapter. Part One: Ethical Systems. I. Moral Cognition. II. Ethical Systems and Boolean Algebra. III. Boolean Algebra, Exponent, Logarithm. IV. Individuals, Reflexion, and Interaction. V. Automata with Semantics and Ethical Status. VI. A Formal Representation of Doubts and Feelings. VII. A Formal Comparison of Ethical Systems: Guilt, Condemnation, Doubt. VIII. A Formal Comparison of Ethical Systems: Doubts and Ethical Status. IX. Ethical Analysis of Artistic and Propagandistic Literature. X. Experimental Analysis of Normative Individuals. XI. The Principle of Maximization of the Ethical Status of One's Image of Oneself. XII. Feelings and Sacrifices. XIII. Formal Connections between Modules of Inner Structures and Individuals. XIV. Interaction. Activity and Its Measure. XV. Ethical Typology in the Novel Crime and Punishment by Dostoevsky. XVI. Ideology, Morality, and Political Organization. XVII. Generalization. Proof of Existence of Ethically Non-Measurable Situations. Part Two: Moral Choice. I. The Tree-Faced Janus: An Initial Metaphor for the Model of the Subject. II. A Boolean Model of Bipolar Choice. III. Metachoice. IV. Modeling of Awareness. V. The Prisoner's Dilemma. VI. The Morality of Results and the Morality of Means. VII. A Boolean-Linear Model of the Subject. VIII. Examples of Modeling the Process of Choice. IX. Imitation of the Other. X. The subject Controlling His Relationships with Another Subject. XI. Two Aspects of Choice. XII. Generalization of Classical Game Theory of 2x2 Zero-Sum Game. XIII. Risk and Caution. XIV. The Non-Linear Model of the Subject. XV. Subject with a Quadratic Model of the Situation. XVI. Streams of Consciousness and Difference Equations. XVII. Streams of Consciousness and Acts of Awareness Epilogue to Part Two. Appendices. References. Index of Names. Subject Index.

Vladimir A. Lefebvre

Papers

Algebra of conscience

The fundamental structures of human reflexion

The golden section and an algebraic model of ethical cognition

Modeling an experiment on construing self and others

The structure of awareness : toward a symbolic language of human reflexion