Computations in Riemann Geometry

1. Introduction

   • Organization of the book
   • About the Code Examples
   • Conventions
   • Acknowledgments and Mea Culpas

2. Curvature Tensors

3. Curvature Invariants

   • The Schwarzschild Spacetime
   • Invariants in General
   • Invariants of Interest to Us

4. Sⁿ

5. Tⁿ

6. Cosmological Solutions to Einstein's Equations

   • FRW Cosmologies

7. Black Holes

   • Killing Vectors and Null Surfaces
   • Geometry
   • Higher-dimensional Kerr Solutions
   • Invariants for Kerr^D
   • Nonzero Cosmological Constant
   • Schwarzschild/Anti-deSitter in D=4

8. Collapsing Dust

   • Geometry
   • Schwarzschild Limit

9. BPS Membranes in Supergravity

   • Curvature Invariants on Supergravity Membranes

10. Warped Product Spaces

    • Simple Product Metrics

Appendices

11. Geodesics

    • Acceleration, Expansion, Shear and Twist

12. Visual Analysis of Curvature Invariants

    • Other Visualizations

13. Functional Computation

14. Parallel Algebraic Computation

    • PTAH implementation

15. Algebraic Computation without Mathematica

    • Implementation in C or C++
    • Classes used in PTAH
    • PVM - Parallel Virtual Machine
    • Hybridization with Mathematica

16. References

17. Index

    A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

©2005, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

Please send comments or suggestions to the author.