## e-books in General Theory of Relativity category

**Mathematical Relativity**

by

**José Natário**-

**arXiv**,

**2020**

These are lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.

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**1072**views)

**Treatise on Differential Geometry and its role in Relativity Theory**

by

**Subenoy Chakraborty**-

**arXiv.org**,

**2022**

These notes will be helpful to undergraduate and postgraduate students in theoretical physics and in applied mathematics. Modern terminology in differential geometry has been discussed in the book with the motivation of geometrical way of thinking.

(

**3323**views)

**The Mathematical Theory of Relativity**

by

**Arthur Stanley Eddington**-

**Cambridge University Press**,

**1923**

Sir Arthur Eddington here formulates mathematically his conception of the world of physics derived from the theory of relativity. The argument is developed in a form which throws light on the origin and significance of the great laws of physics.

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**6181**views)

**Light Rays, Singularities, and All That**

by

**Edward Witten**-

**arXiv.org**,

**2019**

This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem.

(

**4622**views)

**Dynamical and Hamiltonian Formulation of General Relativity**

by

**Domenico Giulini**-

**arXiv.org**,

**2015**

This text introduces the reader to the reformulation of Einstein's field equations of General Relativity as a constrained evolutionary system of Hamiltonian type and discusses some of its uses, together with some technical and conceptual aspects.

(

**5916**views)

**Metric Relativity and the Dynamical Bridge: highlights of Riemannian geometry in physics**

by

**Mario Novello, Eduardo Bittencourt**-

**arXiv**,

**2015**

We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of research...

(

**5848**views)

**Schwarzschild and Kerr Solutions of Einstein's Field Equation: an introduction**

by

**Christian Heinicke, Friedrich W. Hehl**-

**arXiv**,

**2015**

Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild solution, and into one specific stationary solution, the Kerr solution.

(

**8316**views)

**The Geometry of General Relativity**

by

**Tevian Dray**-

**Oregon State University**,

**2014**

The manuscript emphasizes the use of differential forms, rather than tensors, which are barely mentioned. The focus is on the basic examples, namely the Schwarzschild black hole and the Friedmann-Robertson-Walker cosmological models.

(

**11462**views)

**The Confrontation between General Relativity and Experiment**

by

**Clifford M. Will**-

**arXiv**,

**2014**

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them are reviewed and updated. Tests of general relativity have reached high precision, including the light deflection, the Shapiro time delay, etc.

(

**7734**views)

**A No-Nonsense Introduction to General Relativity**

by

**Sean M. Carroll**,

**2001**

General relativity has a reputation of being extremely difficult. This introduction is a very pragmatic affair, intended to give you some immediate feel for the language of GR. It does not substitute for a deep understanding -- that takes more work.

(

**9036**views)

**Space - Time - Matter**

by

**Hermann Weyl**-

**Methuen & Co.**,

**1922**

A classic of physics -- the first systematic presentation of Einstein's theory of relativity. Long one of the standard texts in the field, this excellent introduction probes deeply into Einstein's general relativity, gravitational waves and energy.

(

**10069**views)

**Foundations of Tensor Analysis for Students of Physics and Engineering With an Introduction to the Theory of Relativity**

by

**Joseph C. Kolecki**-

**Glenn Research Center**,

**2005**

Tensor analysis is useful because of its great generality and compact notation. This monograph provides a conceptual foundation for students of physics and engineering who wish to pursue tensor analysis as part of their advanced studies.

(

**11238**views)

**General Relativity Without Calculus**

by

**Jose Natario**-

**Springer**,

**2012**

This book was written as a guide for a one week course aimed at exceptional students in their final years of secondary education. The course was intended to provide a quick but nontrivial introduction to Einstein's general theory of relativity.

(

**11009**views)

**Advanced General Relativity**

by

**Neil Lambert**-

**King's College London**,

**2009**

Contents: Introduction; Manifolds and Tensors; General Relativity (Derivation, Diffeomorphisms as Gauge Symmetries, Weak Field Limit, Tidal Forces, ...); The Schwarzchild Black Hole; More Black Holes; Non-asymptotically Flat Solutions.

(

**9673**views)

**Spacetime Geometry and General Relativity**

by

**Neil Lambert**-

**King's College London**,

**2011**

This course is meant as introduction to what is widely considered to be the most beautiful and imaginative physical theory ever devised: General Relativity. It is assumed that you have a reasonable knowledge of Special Relativity as well as tensors.

(

**9830**views)

**Mass and Angular Momentum in General Relativity**

by

**J.L. Jaramillo, E. Gourgoulhon**-

**arXiv**,

**2010**

We present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy-momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without symmetries.

(

**9590**views)

**Recent Developments in Gravitational Collapse and Spacetime Singularities**

by

**Pankaj S. Joshi, Daniele Malafarina**-

**arXiv**,

**2012**

The research of recent years has provided considerable clarity and insight on stellar collapse, black holes and the nature and structure of spacetime singularities. In this text, the authors discuss several of these developments here.

(

**11151**views)

**Vector Analysis and the Theory of Relativity**

by

**Francis Dominic Murnaghan**-

**Johns Hopkins press**,

**1922**

This monograph is the outcome of lectures delivered to the graduate department of mathematics of The Johns Hopkins University. Considerations of space have made it somewhat condensed in form, but the mode of presentation is sufficiently novel.

(

**15639**views)

**General Covariance and the Foundations of General Relativity**

by

**John D Norton**-

**University of Pittsburgh**,

**1993**

This text reviews the development of Einstein's thought on general covariance (the fundamental physical principle of GTR), its relation to the foundations of general relativity and the evolution of the continuing debate over his viewpoint.

(

**10330**views)

**General Relativity Notes**

by

**Edmund Bertschinger**-

**MIT**,

**1999**

Working with GR requires some understanding of differential geometry. In this text we will develop the essential mathematics needed to describe physics in curved spacetime. These notes assume familiarity with special relativity.

(

**12261**views)

**Beyond partial differential equations: A course on linear and quasi-linear abstract hyperbolic evolution equations**

by

**Horst R. Beyer**-

**arXiv**,

**2011**

This course introduces the use of semigroup methods in the solution of linear and nonlinear (quasi-linear) hyperbolic partial differential equations, with particular application to wave equations and Hermitian hyperbolic systems.

(

**14295**views)

**Post-Newtonian Theory for the Common Reader**

by

**Eric Poisson**-

**University of Guelph**,

**2007**

From the table of contents: Preliminaries; Integration techniques; First post-Minkowskian approximation; Second post-Minkowskian approximation; Equations of motion; Gravitational waves; Energy radiated and radiation reaction.

(

**10358**views)

**An Advanced Course in General Relativity**

by

**Eric Poisson**-

**University of Guelph**,

**2002**

These lecture notes are suitable for a one-semester course at the graduate level. Table of contents: Fundamentals; Geodesic congruences; hypersurfaces; Lagrangian and Hamiltonian formulations of general relativity; Black holes.

(

**12799**views)

**Spacetime and Fields**

by

**Nikodem J. Poplawski**-

**arXiv**,

**2009**

A self-contained introduction to the classical theory of spacetime and fields. Topics: Spacetime (tensors, affine connection, curvature, metric, Lorentz group, spinors), Fields (principle of least action, action for gravitational field, matter, etc)

(

**10406**views)

**Gravitational Waves**

by

**Alessandra Buonanno**-

**arXiv**,

**2007**

Gravitational-wave (GW) science has entered a new era. Theoretically, the last years have been characterized by numerous major advances. These lectures are envisioned to be an introductory, basic course in gravitational-wave physics.

(

**11795**views)

**General Relativity**

by

**Benjamin Crowell**-

**lightandmatter.com**,

**2010**

This is an undergraduate textbook on general relativity. It is well adapted for self-study, and answers are given in the back of the book for almost all the problems. The ratio of conceptual to mathematical problems is higher than in most books.

(

**13008**views)

**Advanced General Relativity**

by

**Sergei Winitzki**-

**Google Sites**,

**2007**

Topics include: Asymptotic structure of spacetime, conformal diagrams, null surfaces, Raychaudhury equation, black holes, the holographic principle, singularity theorems, Einstein-Hilbert action, energy-momentum tensor, Noether's theorem, etc.

(

**12556**views)

**Lecture Notes on General Relativity**

by

**Matthias Blau**-

**Universitaet Bern**,

**2014**

The first half of the book is dedicated to developing the machinery of tensor calculus and Riemannian geometry required to describe physics in a curved space time. We will then turn to various applications of General Relativity.

(

**13481**views)

**Gravitational Waves, Sources, and Detectors**

by

**Bernard F Schutz, Franco Ricci**-

**arXiv**,

**2010**

Notes of lectures for graduate students, covering the theory of linearized gravitational waves, their sources, and the prospects at the time for detecting gravitational waves. The lectures remain of interest for pedagogical reasons.

(

**9471**views)

**Neutrosophic Methods in General Relativity**

by

**D. Rabounski, F. Smarandache, L. Borissova**-

**Hexis**,

**2005**

Neutrosophy is a theory developed by Florentin Smarandache in 1995, which studies the nature and properties of neutralities. This book applies neutrosophic method to the General Theory of Relativity, aiming to discover new effects hidden before.

(

**9225**views)

**An Introduction to the Theory of Rotating Relativistic Stars**

by

**Eric Gourgoulhon**-

**arXiv**,

**2010**

These notes introduce the theory of rotating stars in general relativity. The focus is on the theoretical foundations, with a detailed discussion of the spacetime symmetries, the choice of coordinates and the derivation of the equations of structure.

(

**12419**views)

**Partial Differential Equations of Physics**

by

**Robert Geroch**-

**arXiv**,

**1996**

All partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. We describe some broad features of systems of differential equations so formulated.

(

**16528**views)

**Introduction to General Relativity**

by

**Gerard 't Hooft**-

**Rinton Press**,

**2010**

The book presents the general relativity as a scheme for describing the gravitational field and the equations it obeys. Starting from physical motivations, curved coordinates are introduced, and then the notion of an affine connection field is added.

(

**14921**views)

**Introduction to the Theory of Black Holes**

by

**Gerard 't Hooft**-

**Utrecht University**,

**2009**

Contents: The Metric of Space and Time; Curved coordinates; A short introduction to General Relativity; Gravity; The Schwarzschild Solution; The Chandrasekhar Limit; Gravitational Collapse; The Reissner-Nordstrom Solution; Horizons; and more.

(

**25887**views)

**Complex Geometry of Nature and General Relativity**

by

**Giampiero Esposito**-

**arXiv**,

**1999**

An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.

(

**17060**views)

**Space, Time and Gravitation: An Outline of the General Relativity Theory**

by

**Arthur Stanley Eddington**-

**Cambridge University Press**,

**1920**

The author gives an account of general relativity theory without introducing anything very technical in the way of mathematics, physics, or philosophy. It is hoped that the book may also appeal to those who have gone into the subject more deeply.

(

**13383**views)

**Gravitational Waves and Black Holes: an Introduction to General Relativity**

by

**J.W. van Holten**-

**arXiv**,

**1997**

General relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than mathematical formalism. Dynamical solutions representing traveling waves and stationary fields of black holes are discussed.

(

**12858**views)

**Introduction to relativistic astrophysics and cosmology through Maple**

by

**V. L. Kalashnikov**-

**arXiv**,

**2001**

The author presents the pedagogical introduction to relativistic astrophysics and cosmology, which is based on computational and graphical resources of Maple 6. The knowledge of basics of general relativity and differential geometry is supposed.

(

**16853**views)

**Lecture Notes on General Relativity**

by

**Sean M. Carroll**-

**University of California**,

**1997**

Lecture notes on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications: gravitational radiation, black holes, and cosmology.

(

**15717**views)

**Introduction to Differential Geometry and General Relativity**

by

**Stefan Waner**,

**2005**

Smooth manifolds and scalar fields, tangent vectors, contravariant and covariant vector fields, tensor fields, Riemannian manifolds, locally Minkowskian manifolds, covariant differentiation, the Riemann curvature tensor, premises of general relativity.

(

**23299**views)

**Semi-Riemann Geometry and General Relativity**

by

**Shlomo Sternberg**,

**2003**

Course notes for an introduction to Riemannian geometry and its principal physical application, Einstein’s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus.

(

**18789**views)