Analytical and Numerical Approaches to Mathematical Relativity

Of course the timelike conjugate locus of a point in a space-time will generally not
be closed, but because of the nonimprisonment property that a nonspacelike
geodesic in a globally hyperbolic space-time must escape from any compact ...

Analytical and Numerical Approaches to Mathematical Relativity

Author: Jörg Frauendiener

Publisher: Springer

ISBN: 354033484X

Page: 281

View: 130

General relativity ranks among the most accurately tested fundamental theories in all of physics. Deficiencies in mathematical and conceptual understanding still exist, hampering further progress. This book collects surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods.

The Conformal Structure of Space Times

14.3, one does not know “where the hypersurface sits in the Kruskal space-time”.
... To display the outcome of such a calculation Hübner and Weaver wrote a code
[7] which calculates geodesics along with the ... 14 Data for the Numerical
Calculation of the Kruskal Space-Time 293 14.5 Numerical Calculation of the
Kruskal ...

The Conformal Structure of Space Times

Author: Jörg Frauendiener

Publisher: Springer Science & Business Media

ISBN: 3540442804

Page: 374

View: 449

Causal relations, and with them the underlying null cone or conformal structure, form a basic ingredient in all general analytical studies of asymptotically flat space-time. The present book reviews these aspects from the analytical, geometrical and numerical points of view. Care has been taken to present the material in a way that will also be accessible to postgraduate students and nonspecialist reseachers from related fields.

Dynamical Spacetimes and Numerical Relativity

The velocity parameter , or spacetime angle of the Lorentz transformation needed
to join the two coordinate systems , is precisely the angle of rattle associated with
the hinge . This skeleton geodesic theory has been put into use in the work of ...

Dynamical Spacetimes and Numerical Relativity

Author: Joan M. Centrella

Publisher: CUP Archive

ISBN: 9780521328609

Page: 465

View: 568

Numerical Relativity

slicing or a time coordinate therefore amounts to making a choice for the lapse
function. ... In later chapters we will observe these and other choices in action
when we study actual simulations that construct numerical spacetimes. ... (4.1) In
the context of numerical relativity this gauge choice is often called geodesic
slicing;the resulting coordinates are also known as Gaussian-normal coordinates
.4 Recall ...

Numerical Relativity

Author: Thomas W. Baumgarte

Publisher: Cambridge University Press

ISBN: 1139643177

Page:

View: 899

Aimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad survey of its challenges and achievements. Assuming only a basic knowledge of classical general relativity, the book develops the mathematical formalism from first principles, and then highlights some of the pioneering simulations involving black holes and neutron stars, gravitational collapse and gravitational waves. The book contains 300 exercises to help readers master new material as it is presented. Numerous illustrations, many in color, assist in visualizing new geometric concepts and highlighting the results of computer simulations. Summary boxes encapsulate some of the most important results for quick reference. Applications covered include calculations of coalescing binary black holes and binary neutron stars, rotating stars, colliding star clusters, gravitational and magnetorotational collapse, critical phenomena, the generation of gravitational waves, and other topics of current physical and astrophysical significance.

Applied Differential Geometry

study of global properties of spacetimes relies to a large extent on the ability to
integrate the geodesic equations. In the absence of exact solutions numerical
integration is often used to get a quantitative picture. However, in the quest for a ...

Applied Differential Geometry

Author:

Publisher:

ISBN: 9814475645

Page:

View: 895

Visualization 92

Virtual Spacetime : An Environment for the Visualization of Curved Spacetimes
via Geodesic Flows Steve Brysont Applied Research Branch , Numerical
Aerodynamics Simulation Division NASA Ames Research Center , MS T045 - 1 ,
Moffett ...

Visualization  92

Author: Arie Kaufman

Publisher: IEEE Computer Society

ISBN: 9780818628979

Page: 446

View: 548

Contains 44 papers concerned with all aspects of this subject, with a focus on interdisciplinary techniques. Explores how visualization is used to extract knowledge from data acquired in a variety of applications. No index. Annotation copyright Book News, Inc. Portland, Or.

Numerical Computation of Black Hole Spacetimes

This procedure reduces the stochastic fluctuations associated with having only a
finite number of particles , giving us smoother results ( 19 ) . 2.3.2 . Geodesic
Equations Since the matter is made up of particles , the equation of motion Vetab
= 0 ...

Numerical Computation of Black Hole Spacetimes

Author: Mark Allen Scheel

Publisher:

ISBN:

Page: 428

View: 386

Physics Briefs

See Entry 26924 explicitly that the bundle connection of the Finsler spacetime
tangent bundle can be made Numerical relativity on a transputer array . ... It is
found that the rational first integral of the geodesic by use of bispinors . A U ( 1 ) ...

Physics Briefs

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Dissertation Abstracts

A number of the properties which are of interest in the physical interpretation of
the space - times found to be in geodesic correspondence are illustrated for a
particular class of spaces . In large measure , this involves an investigation of the
 ...

Dissertation Abstracts

Author:

Publisher:

ISBN:

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View: 257

Collier s Encyclopedia

The geodesics are the pieces from point to point along the path . space - time
analogues of the straight lines of ... from the star line of least resistance , so it is
no longer necessary to appeal to his eye , he would find that the number of
meters ...

Collier s Encyclopedia

Author: Louis Shores

Publisher:

ISBN:

Page:

View: 241

Dissertation Abstracts International

No changes in the structure of null geodesics are recorded , but significant
differences are ... Other differences are evident after constructing a maximal
extension followed by a Penrose diagram for this spacetime . ... Adviser : Michael
A . Strauss Order Number DA3110249 The hydrogen Balmer emission lines are
the most prominent feature in the optical spectra of low redshift Active Galactic
Nuclei ( AGN ) ...

Dissertation Abstracts International

Author:

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View: 554

Mathematical Reviews

In the case of spherically symmetric spacetimes he proves the existence of a
global coordinate system on the corresponding ... Essentially , up to an error of
order n + 1 , a knight reaches the image of the exact diffeomorphism after a
number n of increasingly ... been devoted to the “ isometry character ” of the ten
Killing fields than to their additional property of satisfying the geodesic deviation
equation .

Mathematical Reviews

Author:

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View: 312

Studies in numerical analysis

For Riemannian spacetimes admitting symmetry properties leading to m-th order
first integrals (FI) of geodesies (see ... write the following simple type of field
conservation law generator for a timelike geodesic congruence (If = d^lds): (y/^
gpIT .

Studies in numerical analysis

Author: Cornelius Lanczos

Publisher: Academic Press

ISBN:

Page: 333

View: 565

Papers in honour of Cornelius Lanczos.