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 ...
Author: Jörg Frauendiener
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.
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
 which calculates geodesics along with the ... 14 Data for the Numerical
Calculation of the Kruskal Space-Time 293 14.5 Numerical Calculation of the
Author: Jörg Frauendiener
Publisher: Springer Science & Business Media
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.
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 ...
Author: Thomas W. Baumgarte
Publisher: Cambridge University Press
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.
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 ,
Author: Arie Kaufman
Publisher: IEEE Computer Society
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.
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/^
Author: Cornelius Lanczos
Publisher: Academic Press
Papers in honour of Cornelius Lanczos.