Numerical Relativity: Starting from Scratch

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.

Thomas W. Baumgarte is the William R. Kenan Jr. Professor of Physics at Bowdoin College in Brunswick, Maine. His work in numerical relativity and relativistic astrophysics has been recognized with prizes and fellowships from the Guggenheim Foundation, the Humboldt Foundation, the American Physical Society, and the Simons Foundation. Stuart Shapiro and he have previously co-authored the graduate-level text Numerical Relativity: Solving Einstein's Equations on the Computer (Cambridge, 2010).
Stuart L. Shapiro is a Professor of Physics and Astronomy at the University of Illinois at Urbana-Champaign. He is a leading scientist in theoretical astrophysics and general relativity and has been awarded numerous prizes and honors for his research and teaching, including Sloan and Guggenheim fellowships, IBM Supercomputing awards, and the Hans A. Bethe Prize of the American Physical Society, where he was elected Fellow. Shapiro has published over 400 research papers and, in addition to his writing with Thomas Baumgarte, he is co-author of the classic text Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects (1983).