02192nam a22002771i 450099100426522760753620240125113018.0230227s2021 sz rb 001 0 eng d9783030656850Bibl. Dip.le Aggr. Matematica e Fisica - Sez. Fisicaeng530.1123LC QC173.653.1.52AMS 53-XXNatário, José721266An Introduction to mathematical relativity /José NatárioCham, Switzerland :Springer,c2021viii, 186 p. :ill. ;24 cmLatin American mathematics series. UFSCar subseries,2524-6755Includes bibliographical references and indexPreliminaries -- Exact Solutions -- Causality -- Singularity Theorems -- Cauchy Problems -- Mass in general relativity -- Black Holes -- Appendix: Mathematical Concepts for PhysicistsThis 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 Tecnico (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 in Riemannian geometry (for students of Mathematics) or in general relativity (for those in Physics) can benefit from this bookGeneral relativity (Physics)Mathematics991004265227607536Introduction to mathematical relativity3590963UNISALENTO