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This concise textbook introduces the reader to advanced mathematical aspects of general relativity, covering topics like Penrose diagrams, causality theory, singularity theorems, the Cauchy problem for the Einstein equations, the positive mass theorem, and the laws of black hole thermodynamics. It emerged from lecture notes originally conceived for a one-semester course in Mathematical Relativity which has been taught at the Instituto Superior Técnico (University of Lisbon, Portugal) since 2010 to Masters and Doctorate students in Mathematics and Physics.
Mostly self-contained, and mathematically rigorous, this book can be appealing to graduate students in Mathematics or Physics seeking specialization in general relativity, geometry or partial differential equations. Prerequisites include proficiency in differential geometry and the basic principles of relativity. Readers who are familiar with special relativity and have taken a course either inRiemannian geometry (for students of Mathematics) or in general relativity (for those in Physics) can benefit from this book.
List of contents
- Preface.- Preliminaries.- Exact Solutions.- Causality.- Singularity Theorems.- Cauchy Problems.- Mass in general relativity.- Black Holes.- Appendix: Mathematical Concepts for Physicists.- Bibliography.- Index.
About the author
José Natário
holds a DPhil in Mathematical Sciences (2000) from the University of Oxford, England. He has been an Associate Professor of Mathematics at Instituto Superior Técnico (University of Lisbon, Portugal) since 2010, where he teaches a course in Mathematical Relativity to Master and Doctorate students in Mathematics and Physics. He authored "General Relativity Without Calculus" (2011, ISBN 978-3-642-21451-6) and co-authored "An Introduction to Riemannian Geometry" (2014, ISBN 978-3-319-08665-1), both published by Springer.
Summary
This concise textbook introduces the reader to advanced mathematical aspects of general relativity, covering topics like Penrose diagrams, causality theory, singularity theorems, the Cauchy problem for the Einstein equations, the positive mass theorem, and the laws of black hole thermodynamics. It emerged from lecture notes originally conceived for a one-semester course in Mathematical Relativity which has been taught at the Instituto Superior Técnico (University of Lisbon, Portugal) since 2010 to Masters and Doctorate students in Mathematics and Physics.
Mostly self-contained, and mathematically rigorous, this book can be appealing to graduate students in Mathematics or Physics seeking specialization in general relativity, geometry or partial differential equations. Prerequisites include proficiency in differential geometry and the basic principles of relativity. Readers who are familiar with special relativity and have taken a course either inRiemannian geometry (for students of Mathematics) or in general relativity (for those in Physics) can benefit from this book.
Additional text
“This is a well-organized book that provides advanced students with the appropriate background a comfortable first introduction to important mathematical results of general relativity. … The instructive reading will certainly motivate many students to subsequently expand their scope even further, both thematically and methodologically.” (Wolfgang Hasse, Mathematical Reviews, April, 2022)
Report
"This is a well-organized book that provides advanced students with the appropriate background a comfortable first introduction to important mathematical results of general relativity. ... The instructive reading will certainly motivate many students to subsequently expand their scope even further, both thematically and methodologically." (Wolfgang Hasse, Mathematical Reviews, April, 2022)
