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the black hole equilibrium problem been solved
 in Proc. of the 8th Marcel Grossmann Meeting on Relativistic Astrophysics  MG 8
, 1997
"... Abstract. When the term “black hole ” was originally coined in 1968, it was immediately conjectured that the only pure vacuum equilibrium states were those of the Kerr family. Efforts to confirm this made rapid progress during the “classical phase ” from 1968 to 1975, and some gaps in the argument h ..."
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Abstract. When the term “black hole ” was originally coined in 1968, it was immediately conjectured that the only pure vacuum equilibrium states were those of the Kerr family. Efforts to confirm this made rapid progress during the “classical phase ” from 1968 to 1975, and some gaps in the argument have been closed during more recent years. However the presently available demonstration is still subject to undesirably restrictive assumptions such as nondegeneracy of the horizon, as well as analyticity and causality in the exterior. 1
Energy dominance and the Hawking Ellis vacuum conservation theorem
"... Abstract. At a time when uninhibited speculation about negative tension – and by implication negative mass density – world branes has become commonplace, it seems worthwhile to call attention to the risk involved in sacrificing traditional energy positivity postulates such as are required for the cl ..."
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Abstract. At a time when uninhibited speculation about negative tension – and by implication negative mass density – world branes has become commonplace, it seems worthwhile to call attention to the risk involved in sacrificing traditional energy positivity postulates such as are required for the classical vacuum stability theorem of Hawking and Ellis. As well as recapitulating the technical content of this reassuring (when applicable) theorem, the present article provides a new, rather more economical proof. 1. Introduction. Although overshadowed by other more recent contributions – such as the noboundary recipe for creation of an entire universe – one of the most obvious subjects for reminiscence on the auspicious occasion of this 60th birthday celebration for Stephen Hawking is his central role in the foundation of classical
Fast Quantum Algorithms for Handling Probabilistic and Interval Uncertainty
, 2003
"... this paper, we show how the use of quantum computing can speed up some computations related to interval and probabilistic uncertainty. We end the paper with speculations on whether (and how) "hypothetic" physical devices can compute NPhard problems faster than in exponential time ..."
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Cited by 6 (6 self)
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this paper, we show how the use of quantum computing can speed up some computations related to interval and probabilistic uncertainty. We end the paper with speculations on whether (and how) "hypothetic" physical devices can compute NPhard problems faster than in exponential time
Journal of Theoretics
"... : This paper presents a newly developed feature of mass that with the change of temperature, it is changed not only in quantity but also in the quality. It is proposed and shown herein that an attractive mass will decrease as the temperature increases, until it gets the quality of repulsion after go ..."
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: This paper presents a newly developed feature of mass that with the change of temperature, it is changed not only in quantity but also in the quality. It is proposed and shown herein that an attractive mass will decrease as the temperature increases, until it gets the quality of repulsion after going through the massless state. The change of mass from an attracting mass into a repulsing one represents the fundamental novelty in the mass interactions, and takes them into the natural harmony with all other known interactions in the nature. So, all known interactions in the nature are the attractingrepulsive ones, without exceptions. By introducing such antigravitation into the theory of interactions, the clear and simple way toward the Unified Theory of Fields is opened. Keywords: mass, temperature, relativity, gravitation, attraction, repulsion, antigravity. Introduction Relativity of the body mass, in relation to its temperature, is more amazing than the relativity of the body mas...
Young Collapsed Supernova Remnants: Similarities and Differences in Neutron Stars, Black Holes, and More Exotic Objects
, 2000
"... Abstract. Type Ia supernovae are thought to explode completely, leaving no condensed remnant, only an expanding shell. Other types of supernovae are thought to involve core collapse and are expected to leave a condensed remnant, which could be either a neutron star or a black hole, or just possibly, ..."
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Abstract. Type Ia supernovae are thought to explode completely, leaving no condensed remnant, only an expanding shell. Other types of supernovae are thought to involve core collapse and are expected to leave a condensed remnant, which could be either a neutron star or a black hole, or just possibly, something more exotic, such as a quark or strange star, a naked singularity, a frozen star, a wormhole or a red hole. It has proven surprisingly difficult to determine which type of condensed remnant has been formed in those cases where the diagnostic highly regular pulsar signature of a neutron star is absent. We consider possible observational differences between the two standard candidates, as well as the more speculative alternatives. We classify condensed remnants according to whether they do or do not possess three major features: 1)a hard surface, 2)an event horizon, and 3)a singularity. Black holes and neutron stars differ on all three criteria. Some of the less frequently considered alternatives are ”intermediate, ” in the sense that they possess some of the traits of a black hole and some of the traits of a neutron star. This possibility makes distinguishing the various possibilities even more difficult.
τ l
"... The spinor representation of the Lorentz group does not accept simple generalization with the group GL(4, R) of general linear coordinate transformations. The Dirac equation may be written for an arbitrary choice of a coordinate system and a metric, but the covariant linear transformations of the fo ..."
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The spinor representation of the Lorentz group does not accept simple generalization with the group GL(4, R) of general linear coordinate transformations. The Dirac equation may be written for an arbitrary choice of a coordinate system and a metric, but the covariant linear transformations of the fourcomponent Dirac spinor exist only for isometries. For usual diagonal Minkowski metric the isometry is the Lorentz transformation. On the other hand, it is possible to define the Dirac operator on the space of antisymmetric (exterior) forms, and in such a case the equation is covariant for an arbitrary general linear transformation. The space of the exterior forms is sixteendimensional, but usual Dirac equation is defined for fourdimensional complex space of Dirac spinors. Using suggested analogy, in present paper is discussed possibility to consider the space of Dirac spinors as some “subsystem ” of a bigger space, where the group GL(4, R) of General Relativity acts in a covariant way. For such purposes in this article is considered both Grassmann algebra of complex antisymmetric forms and Clifford algebra of Dirac matrices. Both algebras have same dimension as linear spaces, but different structure of multiplication. The underlying sixteendimensional linear space also may be considered either as space of complex 4 ×4 matrices, or as space of states of two particles: the initial Dirac spinor and some auxiliary system. It is shown also, that such approach is in good agreement with well known idea to consider Dirac spinor as some ideal of Clifford algebra. Some other possible implications of given model are also discussed. r
τ l
"... The spinor representation of the Lorentz group does not accept simple generalization with the group GL(4, R) of general linear coordinate transformations. The Dirac equation may be written for an arbitrary choice of a coordinate system and a metric, but the covariant linear transformations of the fo ..."
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The spinor representation of the Lorentz group does not accept simple generalization with the group GL(4, R) of general linear coordinate transformations. The Dirac equation may be written for an arbitrary choice of a coordinate system and a metric, but the covariant linear transformations of the fourcomponent Dirac spinor exist only for isometries. For usual diagonal Minkowski metric the isometry is the Lorentz transformation. On the other hand, it is possible to define the Dirac operator on the space of antisymmetric (exterior) forms, and in such a case the equation is covariant for an arbitrary general linear transformation. The space of the exterior forms is sixteendimensional, but usual Dirac equation is defined for fourdimensional complex space of Dirac spinors. Using suggested analogy, in present paper is discussed possibility to consider the space of Dirac spinor as some “subsystem ” of a bigger space, where the group GL(4, R) of general relativity acts in a covariant way. For such purposes in this article is considered both Grassmann algebra of complex antisymmetric forms and Clifford algebra of Dirac matrices. Both algebras have same dimension as linear spaces, but different structure of multiplication. The underlying sixteendimensional linear space also may be considered either as space of complex 4 × 4 matrices, or as space of states of two particles, there state of initial Dirac spinor is situated as subsystem. It is shown also, that such approach is in good agreement with well known idea to consider Dirac spinor as some ideal of Clifford algebra. Some other possible implications of given model are also discussed. r
Bürgi, Jost B 1
, 1632
"... Jost Bürgi was a clock maker, astronomer, and applied mathematician. His father was probably a fitter. Very little seems to be known about his life before 1579. It is probable that Bürgi obtained much of his knowledge in Strassburg, one of his teachers being the Swiss mathematician Konrad Dasypodius ..."
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Jost Bürgi was a clock maker, astronomer, and applied mathematician. His father was probably a fitter. Very little seems to be known about his life before 1579. It is probable that Bürgi obtained much of his knowledge in Strassburg, one of his teachers being the Swiss mathematician Konrad Dasypodius. An indication that he did not get a systematic education is the fact that Bürgi did not know Latin, the scientific language of his time. Nevertheless, he made lasting scientific contributions that prompted some biographers to call him the “Swiss Archimedes. ” Bürgi was married first to the daughter of David Bramer, then in 1611, married Catharina Braun. Bürgi developed a theory of logarithms independently of his Scottish contemporary John Napier. Napier’s logarithms were published in 1614; Burgi ’ s were published in 1620. The objective of both approaches was to simplify mathematical calculations. While Napier’s approach was algebraic, Bürgi’s point of view was geometric. It is believed that Bürgi created a table of logarithms before Napier by several years, but did not publish it until later in his book Tafeln arithmetischer und geometrischer Zahlenfolgen mit einer gründlichen Erlüterungen, wie sie zu verstehen sind und gebraucht werden können. Indications that Bürgi knew about logarithms earlier in 1588 can be obtained from a letter of the astronomer Nicholaus Bär (Raimarus Ursus), who explains that Bürgi had a method to simplify his calculations using logarithms. Logarithms paved the way for slide rules because the identity log(a·b) = log(a) + log(b) allows one to compute the product of two numbers a and b as an addition. Bürgi also computed sintables. These tables,