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Author: Nicholas Layden
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
A new conjecture for geometric horizons has been introduced which may provide a potential alternative to using apparent horizons and related surfaces for analyzing the dynamics of black hole spacetimes. In particular, using two examples of black hole formation in a collapsing universe in the Szekeres spacetime, the formation, evolution, and detection of geometric horizons are shown. In addition, a function for detecting apparent horizons in the Szekeres spacetime is also considered, and it is shown that the apparent horizon in the Szekeres model, is in fact, a geometric horizon. The Cartan-Karlhede algorithm for determining local equivalences of spacetimes is used to compute an invariant frame in the Newman Penrose frame formalism, and Cartan invariants derived from the spacetime in this frame are shown to detect the geometric horizons under various conditions on the curvature tensors of the spacetime. One model for primordial black hole formation and another for galactic black hole formation are considered with non-zero cosmological constants, generalizing work published previously on these models with zero cosmological constant. Future work utilizing geometric horizons may provide benefits in gravitational wave research involving black hole mergers.
Author: Nicholas Layden
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
A new conjecture for geometric horizons has been introduced which may provide a potential alternative to using apparent horizons and related surfaces for analyzing the dynamics of black hole spacetimes. In particular, using two examples of black hole formation in a collapsing universe in the Szekeres spacetime, the formation, evolution, and detection of geometric horizons are shown. In addition, a function for detecting apparent horizons in the Szekeres spacetime is also considered, and it is shown that the apparent horizon in the Szekeres model, is in fact, a geometric horizon. The Cartan-Karlhede algorithm for determining local equivalences of spacetimes is used to compute an invariant frame in the Newman Penrose frame formalism, and Cartan invariants derived from the spacetime in this frame are shown to detect the geometric horizons under various conditions on the curvature tensors of the spacetime. One model for primordial black hole formation and another for galactic black hole formation are considered with non-zero cosmological constants, generalizing work published previously on these models with zero cosmological constant. Future work utilizing geometric horizons may provide benefits in gravitational wave research involving black hole mergers.
Author: Marcus Kriele
Publisher: Springer Science & Business Media
ISBN: 3540663770
Category : Mathematics
Languages : en
Pages : 444
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Book Description
This textbook is for mathematicians and mathematical physicists and is mainly concerned with the physical justification of both the mathematical framework and the foundations of the theory of general relativity. Previous knowledge of the relevant physics is not assumed. This book is also suitable as an introduction to pseudo-Riemannian geometry with emphasis on geometrical concepts. A significant part of the text is devoted to the discussion of causality and singularity theorems. The insights obtained are applied to black hole astrophysics, thereby making the connection to current active research in mathematical physics and cosmology.
Author: Patrick Suppes
Publisher: Springer Science & Business Media
ISBN: 9789027703866
Category : Philosophy
Languages : en
Pages : 448
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Book Description
The articles in this volume have been stimulated in two different ways. More than two years ago the editor of Synthese, laakko Hintikka, an nounced a special issue devoted to space and time, and articles were solicited. Part of the reason for that announcement was also the second source of papers. Several years ago I gave a seminar on special relativity at Stanford, and the papers by Domotor, Harrison, Hudgin, Latzer and myself partially arose out of discussion in that seminar. All of the papers except those of Griinbaum, Fine, the second paper of Friedman, and the paper of Adams appeared in a special double issue of Synthese (24 (1972), Nos. 1-2). I am pleased to have been able to add the four additional papers mentioned in making the special issue a volume in the Synthese Library. Of these four additional articles, only the one by Fine has pre viously appeared in print (Synthese 22 (1971),448--481); its relevance to the present volume is apparent. In preparing the papers for publication and in carrying out the various editorIal chores of such a task, I am very much indebted to Mrs. Lillian O'Toole for her extensive assistance. INTRODUCTION The philosophy of space and time has been of permanent importance in philosophy, and most of the major historical figures in philosophy, such as Aristotle, Descartes and Kant, have had a good deal to say about the nature of space and time.
Author: Gregory L. Naber
Publisher: Cambridge University Press
ISBN: 9780521336123
Category : Mathematics
Languages : en
Pages : 196
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Book Description
An elementary introduction to the geometrical methods and notions used in special and general relativity. Emphasizes the ideas concerned with structure of space-time that play a role in Penrose-Hawking singularity theorems.
Author: Iva Stavrov
Publisher: American Mathematical Soc.
ISBN: 1470456281
Category : Education
Languages : en
Pages : 243
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Book Description
This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations. After addressing concepts in geometry such as metrics, covariant differentiation, tensor calculus and curvature, the book explains the mathematical framework for both special and general relativity. Relativistic concepts discussed include (initial value formulation of) the Einstein equations, stress-energy tensor, Schwarzschild space-time, ADM mass and geodesic incompleteness. The concluding chapters of the book introduce the reader to geometric analysis: original results of the author and her undergraduate student collaborators illustrate how methods of analysis and differential equations are used in addressing questions from geometry and relativity. The book is mostly self-contained and the reader is only expected to have a solid foundation in multivariable and vector calculus and linear algebra. The material in this book was first developed for the 2013 summer program in geometric analysis at the Park City Math Institute, and was recently modified and expanded to reflect the author's experience of teaching mathematical general relativity to advanced undergraduates at Lewis & Clark College.
Author: Rafael Ferraro
Publisher: Springer Science & Business Media
ISBN: 0387699465
Category : Science
Languages : en
Pages : 322
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Book Description
This excellent textbook offers a unique take on relativity theory, setting it in its historical context. Ideal for those interested in relativity and the history of physics, the book contains a complete account of special relativity that begins with the historical analysis of the reasons that led to a change in our view of space and time. Its aim is to foster a deep understanding of relativistic spacetime and its consequences for Dynamics.
Author: Dan A. Lee
Publisher: American Mathematical Society
ISBN: 1470466236
Category : Mathematics
Languages : en
Pages : 377
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Book Description
Many problems in general relativity are essentially geometric in nature, in the sense that they can be understood in terms of Riemannian geometry and partial differential equations. This book is centered around the study of mass in general relativity using the techniques of geometric analysis. Specifically, it provides a comprehensive treatment of the positive mass theorem and closely related results, such as the Penrose inequality, drawing on a variety of tools used in this area of research, including minimal hypersurfaces, conformal geometry, inverse mean curvature flow, conformal flow, spinors and the Dirac operator, marginally outer trapped surfaces, and density theorems. This is the first time these topics have been gathered into a single place and presented with an advanced graduate student audience in mind; several dozen exercises are also included. The main prerequisite for this book is a working understanding of Riemannian geometry and basic knowledge of elliptic linear partial differential equations, with only minimal prior knowledge of physics required. The second part of the book includes a short crash course on general relativity, which provides background for the study of asymptotically flat initial data sets satisfying the dominant energy condition.
Author: Krishan L. Duggal
Publisher: Springer Science & Business Media
ISBN: 3034602510
Category : Mathematics
Languages : en
Pages : 484
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Book Description
This book presents research on the latest developments in differential geometry of lightlike (degenerate) subspaces. The main focus is on hypersurfaces and a variety of submanifolds of indefinite Kählerian, Sasakian and quaternion Kähler manifolds.
Author: Jochen Brüning
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110452154
Category : Mathematics
Languages : en
Pages : 518
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Book Description
This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity
Author: Hans Stephani
Publisher: Cambridge University Press
ISBN: 9781139435024
Category : Science
Languages : en
Pages : 94
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Book Description
A paperback edition of a classic text, this book contains six new chapters, covering generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics.
