Numerical Relativity: Starting from Scratch

A pedagogical and accessible introduction to numerical relativity, the key tool to model gravitational waves and black hole mergers.

Thomas W. Baumgarte (Author), Stuart L. Shapiro (Author)

9781108844116, Cambridge University Press

Hardback, published 8 April 2021

234 pages
23.5 x 15.5 x 1.3 cm, 0.52 kg

'Black holes and gravitational waves are, thanks to new observations, fast-advancing frontiers of astronomy that attract wide interest. Their implications are best addressed by powerful computers, so this text, by two acknowledged world experts, is especially welcome and timely.' Martin Rees, Astronomer Royal; author of Gravity's Fatal Attraction

Numerical relativity has emerged as the key tool to model gravitational waves - recently detected for the first time - that are emitted when black holes or neutron stars collide. This book provides a pedagogical, accessible, and concise introduction to the subject. Relying heavily on analogies with Newtonian gravity, scalar fields and electromagnetic fields, it introduces key concepts of numerical relativity in a context familiar to readers without prior expertise in general relativity. Readers can explore these concepts by working through numerous exercises, and can see them 'in action' by experimenting with the accompanying Python sample codes, and so develop familiarity with many techniques commonly employed by publicly available numerical relativity codes. This is an attractive, student-friendly resource for short courses on numerical relativity, as well as providing supplementary reading for courses on general relativity and computational physics.

Preface
1. Newton's and Einstein's gravity
2. Foliations of spacetime: constraint and evolution equations
3. Solving the constraint equations
4 Solving the evolution equations
5. Numerical simulations of black-hole binaries
Epilogue
Appendix A. A brief review of tensor properties
Appendix B. A brief introduction to some numerical techniques
Appendix C. A very brief introduction to matter sources
Appendix D. A summary of important results
Appendix E. Answers to selected problems
References
Index.

Subject Areas: Astrophysics [PHVB], Relativity physics [PHR], Cosmology & the universe [PGK], Mathematical modelling [PBWH]