46,268 research outputs found
What Is the Validity Domain of Einstein’s Equations? Distributional Solutions over Singularities and Topological Links in Geometrodynamics
The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions
Interval valued (\in,\ivq)-fuzzy filters of pseudo -algebras
We introduce the concept of quasi-coincidence of a fuzzy interval value with
an interval valued fuzzy set. By using this new idea, we introduce the notions
of interval valued (\in,\ivq)-fuzzy filters of pseudo -algebras and
investigate some of their related properties. Some characterization theorems of
these generalized interval valued fuzzy filters are derived. The relationship
among these generalized interval valued fuzzy filters of pseudo -algebras
is considered. Finally, we consider the concept of implication-based interval
valued fuzzy implicative filters of pseudo -algebras, in particular, the
implication operators in Lukasiewicz system of continuous-valued logic are
discussed
Multinational perspectives on information technology from academia and industry
As the term \u27information technology\u27 has many meanings for various stakeholders and continues to evolve, this work presents a comprehensive approach for developing curriculum guidelines for rigorous, high quality, bachelor\u27s degree programs in information technology (IT) to prepare successful graduates for a future global technological society. The aim is to address three research questions in the context of IT concerning (1) the educational frameworks relevant for academics and students of IT, (2) the pathways into IT programs, and (3) graduates\u27 preparation for meeting future technologies. The analysis of current trends comes from survey data of IT faculty members and professional IT industry leaders. With these analyses, the IT Model Curricula of CC2005, IT2008, IT2017, extensive literature review, and the multinational insights of the authors into the status of IT, this paper presents a comprehensive overview and discussion of future directions of global IT education toward 2025
Extended symmetries at the black hole horizon
We prove that non-extremal black holes in four-dimensional general relativity exhibit an infinite-dimensional symmetry in their near horizon region. By prescribing a physically sensible set of boundary conditions at the horizon, we derive the algebra of asymptotic Killing vectors, which is shown to be infinite-dimensional and includes, in particular, two sets of supertranslations and two mutually commuting copies of the Virasoro algebra. We define the surface charges associated to the asymptotic diffeomorphisms that preserve the boundary conditions and discuss the subtleties of this definition, such as the integrability conditions and the correct definition of the Dirac brackets. When evaluated on the stationary solutions, the only non-vanishing charges are the zero-modes. One of them reproduces the Bekenstein-Hawking entropy of Kerr black holes. We also study the extremal limit, recovering the NHEK geometry. In this singular case, where the algebra of charges and the integrability conditions get modified, we find that the computation of the zero-modes correctly reproduces the black hole entropy. Furthermore, we analyze the case of three spacetime dimensions, in which the integrability conditions notably simplify and the field equations can be solved analytically to produce a family of exact solutions that realize the boundary conditions explicitly. We examine other features, such as the form of the algebra in the extremal limit and the relation to other works in the literature.Fil: Donnay, Laura. UniversitĂ© Libre de Bruxelles; BĂ©lgicaFil: Giribet, Gaston Enrique. UniversitĂ© Libre de Bruxelles; BĂ©lgica. Pontificia Universidad CatĂłlica de ValparaĂso; Chile. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Oficina de CoordinaciĂłn Administrativa Ciudad Universitaria. Instituto de FĂsica de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de FĂsica de Buenos Aires; ArgentinaFil: González, Alejandro Hernán. UniversitĂ© Libre de Bruxelles; BĂ©lgicaFil: Pino, Miguel. Universidad de Santiago de Chile; Chil
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