An Introduction to Mathematical Relativity

Beschreibung

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 in Riemannian geometry (for students of Mathematics) or in general relativity (for those in Physics) can benefit from this book.

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.


Offers a view on the advanced mathematical aspects of general relativity Aimed to graduate students in Mathematics and Physics with special interest on the field Concentrates on the simplest versions of the results, avoiding unnecessary complexity

Autor*in

José Natário

Themen in »An Introduction to Mathematical Relativity«

Penrose diagrams causality theory singularity theorems Cauchy problem Einstein equations positive mass theorem Penrose inequality black hole thermodynamics

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“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)
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