An Introduction To Mathematical Relativity
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An Introduction to Mathematical Relativity
Author | : José Natário |
Publsiher | : Springer Nature |
Total Pages | : 186 |
Release | : 2021-03-24 |
Genre | : Mathematics |
ISBN | : 9783030656836 |
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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 in Riemannian geometry (for students of Mathematics) or in general relativity (for those in Physics) can benefit from this book.
An Introduction to General Relativity
Author | : L. P. Hughston,K. P. Tod |
Publsiher | : Cambridge University Press |
Total Pages | : 196 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 052133943X |
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This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to each chapter, some of which extend the development given in the text.
Spacetime and Geometry
Author | : Sean M. Carroll |
Publsiher | : Cambridge University Press |
Total Pages | : 529 |
Release | : 2019-08-08 |
Genre | : Science |
ISBN | : 9781108488396 |
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An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.
A Mathematical Introduction To General Relativity
Author | : Amol Sasane |
Publsiher | : World Scientific |
Total Pages | : 500 |
Release | : 2021-08-10 |
Genre | : Science |
ISBN | : 9789811243790 |
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The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe.Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to the (over 200) exercises are included.
Gravity
Author | : James B. Hartle |
Publsiher | : Cambridge University Press |
Total Pages | : 605 |
Release | : 2021-06-24 |
Genre | : Science |
ISBN | : 9781316517543 |
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Best-selling, accessible physics-first introduction to GR uses minimal new mathematics and begins with the essential physical applications.
An Introduction to General Relativity and Cosmology
Author | : Jerzy Plebanski,Andrzej Krasinski |
Publsiher | : Cambridge University Press |
Total Pages | : 0 |
Release | : 2012-09-13 |
Genre | : Science |
ISBN | : 1107407362 |
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General relativity is a cornerstone of modern physics, and is of major importance in its applications to cosmology. Plebanski and Krasinski are experts in the field and provide a thorough introduction to general relativity, guiding the reader through complete derivations of the most important results. Providing coverage from a unique viewpoint, geometrical, physical and astrophysical properties of inhomogeneous cosmological models are all systematically and clearly presented, allowing the reader to follow and verify all derivations. Many topics are included that are not found in other textbooks.
General Relativity
Author | : Robert M. Wald |
Publsiher | : University of Chicago Press |
Total Pages | : 507 |
Release | : 2010-05-15 |
Genre | : Science |
ISBN | : 9780226870373 |
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"Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful. The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."—S. Chandrasekhar "A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."—L. P. Hughston, Times Higher Education Supplement "Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."—James W. York, Physics Today
The Geometry of Spacetime
Author | : James J. Callahan |
Publsiher | : Springer Science & Business Media |
Total Pages | : 474 |
Release | : 2013-03-09 |
Genre | : Science |
ISBN | : 9781475767360 |
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Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.