Covariant Physics: From Classical Mechanics to General Relativity and BeyondOxford University Press, 2021 M03 2 - 400 pages Covariant Physics: From Classical Mechanics to General Relativity and Beyond endeavours to provide undergraduate students as well as self-learners with training in the fundamentals of the modern theories of spacetime, most notably the general theory of relativity as well as physics in curved spacetime backgrounds in general. This text does so with the barest of mathematical preparation. In fact, very little beyond multivariable calculus and a bit of linear algebra is assumed. Throughout this textbook, the main theme tying the various topics is the so-called principle of covariance - a fundamental symmetry of physics that one rarely encounters in undergraduate texts. The material is introduced very gradually, starting with the simplest of high school mathematics, and moving through the more intense notions of tensor calculus, geometry, and differential forms with ease. Familiar notions from classical mechanics and electrodynamics are used to increase familiarity with the advanced mathematical ideas, and to emphasize the unity of all of physics under the single principle of covariance. The mathematical and physical techniques developed in this book should allow students to perform research in various fields of theoretical physics as early as their sophomore year in college. The language the reader will learn in this book is the foundational mathematical language of many modern branches of physics, and as such should allow them to read and generally understand many modern physics papers. |
Contents
1 | |
Tensors | 41 |
Classical Covariance | 78 |
Special Covariance | 116 |
General Covariance | 164 |
Physics in Curved Spacetime | 211 |
Riemann and Einstein | 254 |
Other editions - View all
Covariant Physics: From Classical Mechanics to General Relativity and Beyond Moataz Emam Limited preview - 2021 |
Covariant Physics: From Classical Mechanics to General Relativity and Beyond Moataz H. Emam No preview available - 2021 |
Common terms and phrases
acceleration action apply arbitrary assume basis becomes black hole calculation called components consider constant coordinate system covariant curved defined definition depending derivative described differential dimensions direction discussed effect Einstein energy equations equivalent event exactly example Exercise exist expression exterior derivative fact field flat force frame function geodesic given gives gravitational Hence indices integral known leads light manifold mass means mechanics metric momentum motion moving natural Newtonian object observer origin parallel particle physics possible potential problem quantity radius reader reference relativistic relativity require respect rest rotations satisfy scalar Schwarzschild shown side simply so-called solution space spacetime special relativity speed sphere spherical stress surface symbols tensor term theory transformation true units universe usual vanishes vector write