Spacetime physics -- Physics in flat spacetime -- The mathematics of curved spacetime -- Einstein's geometric theory of gravity -- Relativistic stars -- The universe -- Gravitational collapse and black holes -- Gravitational waves -- Experimental tests of general relativity -- Frontiers
This is an introductory book on the general theory of relativity based partly on lectures given to students of M.Sc. Physics at my university. The book is divided into three parts. The ?rst part is a preliminary course on general relativity with minimum preparation. The second part builds the ma- ematical background and the third part deals with topics where mathematics developed in the second part is needed. The ?rst chapter gives a general background and introduction. This is f- lowed by an introduction to curvature through Gauss’ Theorema Egregium. This theorem expresses the curvature of a two-dimensional surface in terms of intrinsic quantitiesrelatedtothein?nitesimaldistancefunctiononthesurface.Thestudent isintroducedtothemetrictensor,Christo?elsymbolsandRiemanncurvaturet- sor by elementary methods in the familiar and visualizable case of two dimensions. This early introduction to geometric quantities equips a student to learn simpler topics in general relativity like the Newtonian limit, red shift, the Schwarzschild solution, precession of the perihelion and bending of light in a gravitational ?eld. Part II (chapters 5 to 10) is an introduction to Riemannian geometry as - quired by general relativity. This is done from the beginning, starting with vectors and tensors. I believe that students of physics grasp physical concepts better if they are not shaky about the mathematics involved.
Gravity and Gravitation is a physics book that is written in a form that is easy to understand for high school and beginning college students, as well as science buffs. It is based on the lessons from the School for Champions educational website.The book explains the principles of gravity and gravitation, shows derivations of important gravity equations, and provides applications of those equations. It also compares the different theories of gravitation, from those of Newton to Einstein to present-day concepts.
This is a book about physics, written for mathematicians. The readers we have in mind can be roughly described as those who: I. are mathematics graduate students with some knowledge of global differential geometry 2. have had the equivalent of freshman physics, and find popular accounts of astrophysics and cosmology interesting 3. appreciate mathematical elarity, but are willing to accept physical motiva tions for the mathematics in place of mathematical ones 4. are willing to spend time and effort mastering certain technical details, such as those in Section 1. 1. Each book disappoints so me readers. This one will disappoint: 1. physicists who want to use this book as a first course on differential geometry 2. mathematicians who think Lorentzian manifolds are wholly similar to Riemannian ones, or that, given a sufficiently good mathematical back ground, the essentials of a subject !ike cosmology can be learned without so me hard work on boring detaiis 3. those who believe vague philosophical arguments have more than historical and heuristic significance, that general relativity should somehow be "proved," or that axiomatization of this subject is useful 4. those who want an encyclopedic treatment (the books by Hawking-Ellis [1], Penrose [1], Weinberg [1], and Misner-Thorne-Wheeler [I] go further into the subject than we do; see also the survey article, Sachs-Wu [1]). 5. mathematicians who want to learn quantum physics or unified fieId theory (unfortunateIy, quantum physics texts all seem either to be for physicists, or merely concerned with formaI mathematics).
"This introductory, algebra-based, two-semester college physics book is grounded with real-world examples, illustrations, and explanations to help students grasp key, fundamental physics concepts. ... This online, fully editable and customizable title includes learning objectives, concept questions, links to labs and simulations, and ample practice opportunities to solve traditional physics application problems."--Website of book.
In Topics in the Foundations of General Relativity and Newtonian Gravitation Theory, David B. Malament presents the basic logical-mathematical structure of general relativity and considers a number of special topics concerning the foundations of general relativity and its relation to Newtonian gravitation theory. These special topics include the geometrized formulation of Newtonian theory (also known as Newton-Cartan theory), the concept of rotation in general relativity, and Gödel spacetime. One of the highlights of the book is a no-go theorem that can be understood to show that there is no criterion of orbital rotation in general relativity that fully answers to our classical intuitions. Topics is intended for both students and researchers in mathematical physics and philosophy of science.
Newtons theory of gravitation is the grandest and the most enduring physical theory ever created. Today, more than 300 years after it was first conceived, Newton''s theory of gravitation is still the basic working theory of astronomers and of all the scientists dealing with space exploration and celestial mechanics. However, Newton''s theory of gravitation has serious defects: it is incapable of accounting for certain fine details of planetary motion; it does not provide any information on the temporal aspect of gravitational interactions; it cannot be reconciled with the principle of causality and with the law of conservation of momentum when it is applied to time-dependent gravitational systems.This book extends and generalizes Newton''s theory of gravitation, makes it free from the above defects, makes it fully applicable to all possible gravitational systems, and provides a large variety of methods for calculating gravitational interactions between moving or stationary bodies of all shapes, sizes and configurations.The starting point of the generalization of Newton''s theory of gravitation developed in this book is the idea that gravitational interactions are mediated by two force fields: the gravitational field proper created by all masses and acting upon all masses, and the "cogravitational" field created by moving masses only and acting upon moving masses only. In accordance with the principle of causality, the two fields are represented by retarded field integrals, which, for static or slowly-varying gravitational systems, yield the ordinary Newtonian gravitational field.An immediate consequence of the generalized Newtonian theory of gravitation developed on this basis is that gravitational interactions normally involve at least five different forces associated with velocities, accelerations and rotations of interacting bodies. The effects of these forces are quite remarkable. Some examples: a fast-moving mass passing a spherically-symmetric body causes the latter to rotate; a mass moving with rapidly-decreasing velocity exerts both an attractive and a repulsive force on neighboring bodies; a rotating mass that is suddenly stopped causes neighboring bodies to rotate; the differential rotation of the Sun is caused by the planets orbiting around it.The generalized theory of gravitation is fully compatible with the laws of conservation of energy and momentum. A very important result of this compatibility is the definitive explanation of the process of conversion of gravitational field energy into the kinetic energy of bodies moving under the action of gravitational fields.The generalized theory of gravitation predicts the existence of gravitation-cogravitational waves and explains how such waves can be generated.The generalized theory of gravitation also indicates the existence of antigravitational (repulsive) fields and mass formations. A cosmological consequence of such fields and mass formations is a periodic expansion and contraction of the Universe. Another consequence is that the actual mass of the Universe may be much larger than the mass revealed by an analysis of gravitational attraction in the galaxies.It is natural to compare the various consequences of the generalized theory of gravitation with the consequences of the general relativity theory. In this regard the following three remarks should be made.First, there are no observable gravitational effects revealed by the general relativity theory that do not have their counterparts in the generalized theory of gravitation.Second, the generalized theory of gravitation describes a vastly larger number of gravitational effects than those described by the general relativity theory.Third, numerical values for gravitational effects predicted by the general relativity theory are usually different from the corresponding values predicted by the generalized theory of gravitation; the difference is almost always a consequence of greater complexity and depth of gravitational interactions revealed by the generalized theory of gravitation.Although this book presents the results of original research, it is written in the style of a textbook and contains numerous illustrative examples demonstrating various applications of the generalized Newtonian theory of gravitation developed in the book.
This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence and stresses the global aspects of cosmology. Suitable for independent study as well as for courses in differential geometry, relativity, and cosmology. 1979 edition.