Analytical and Numerical Approaches to Mathematical Relativity

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.

Analytical and Numerical Approaches to Mathematical Relativity

Author: Jörg Frauendiener

Publisher: Springer

ISBN: 354033484X

Page: 281

View: 918

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.

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

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Page: 428

View: 569

Energy Research Abstracts

6570 Theoretical and Mathematical Physics Number Fields are of such a type, an
application is demonstrated using the ... Numerical examples are given. ... 337O6
(KFK-1989-52/B) On the minimum uncertainty of space-time geodesics. Diosi ...

Energy Research Abstracts

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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: 100

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.

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

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Nuclear Science Abstracts

This structure is integrable if and only if the spacetime admits two geodesic and
shearfree null congruences , thus in particular ... Numerical techniques for
calculating radiation patterns from the propagation equations are discussed ,
including ...

Nuclear Science Abstracts

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Nuclear Science Abstracts

Numerical computations for gravitational radiation from a charge executing
circular orbits in a Coulomb field, given in a recent paper, are corrected. ... The
Feynman spacetime interpretation of quantum field theory is extended to the
case of general Riemann ... The metric of type D is determined explicitly and also
the metric of type III for which the nonrepeated eigenvector of the Weyl tensor is
geodesic.

Nuclear Science Abstracts

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Abstracts of Contributed Papers

... No and No ' say , and the field equations are integrated numerically to
determine space - time to the future of both No ... of caustics ( where null
geodesics focus and intersect each other ) , although special techniques have
been developed ...

Abstracts of Contributed Papers

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Page: 760

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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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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

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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: Brendan Kevin Patrick Scaife

Publisher: Academic Press

ISBN:

Page: 333

View: 735

Papers in honour of Cornelius Lanczos.

Progress of Theoretical Physics

Geodesics in Kerr geometry $ 9 . Source terms § 10 . ... Here the birth means the
work by Smarr ( 1977 ) for two black hole collision as it was the first numerically
generated non - spherical space - times with asymptotic flatness . In Kyoto , the ...

Progress of Theoretical Physics

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Proceedings of the Royal Society of London

Now consider a spacelike region B enclosing r = 3M and examine solutions of ( 1
) that , for convenience , have unit energy within B initially , Ex ( 0 ) = 1 , where EX
( t ) is the energy within B at time t . Suppose we concentrate the energy within a
narrow tube of null geodesics . Initially the tube remains within B and the energy
E ... This formula is also consistent with the numerical work of Leaver ( 1985 )
who considered m < 12 . Next consider what would have happened if the r = 3M ...

Proceedings of the Royal Society of London

Author: Royal Society (Great Britain)

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View: 938