Relativity in Modern Physics

This comprehensive textbook on relativity integrates Newtonian physics, special relativity and general relativity into a single book that emphasizes the deep underlying principles common to them all, yet explains how they are applied in different ways in these three contexts. Newton's ideas about how to represent space and time, his laws of dynamics, and his theory of gravitation established the conceptual foundation from which modern physics developed. Book I in this volume offers undergraduates a modern view of Newtonian theory, emphasizing those aspects needed for understanding quantum and relativistic contemporary physics. In 1905, Albert Einstein proposed a novel representation of space and time, special relativity. Book II presents relativistic dynamics in inertial and accelerated frames, as well as a detailed overview of Maxwell's theory of electromagnetism. This provides undergraduate and graduate students with the background necessary for studying particle and accelerator physics, astrophysics and Einstein's theory of general relativity. In 1915, Einstein proposed a new theory of gravitation, general relativity. Book III in this volume develops the geometrical framework in which Einstein's equations are formulated, and presents several key applications: black holes, gravitational radiation, and cosmology, which will prepare graduate students to carry out research in relativistic astrophysics, gravitational wave astronomy, and cosmology.

1 - Cartesian coordinates
2 - Vector geometry
3 - Curvilinear coordinates
4 - Differential geometry
5 - Equations of motion
6 - Dynamics of massive systems
7 - Conservation laws
8 - Lagrangian mechanics
9 - Hamiltonian mechanics
10 - Kinetic theory
11 - The law of gravitation
12 - The Kepler problem
13 - The N-body problem
14 - Deformations of celestial bodies
15 - Self-gravitating fluids
16 - Newtonian cosmology
17 - Light in Newtonian theory
1 - Minkowski spacetime
2 - The kinematics of a point particle
3 - The kinematics of light
4 - The wave vector of light
5 - Accelerated frames
5 - Dynamics of a point particle
6 - Dynamics of a point particle
7 - Rotating systems
8 - Fields and matter
9 - The classical scalar field
10 - The Nordstrom theory
11 - The Lorentz force
12 - The Maxwell equations
13 - Constant fields
14 - The free field
15 - Electromagnetic waves
16 - Waves in a medium
17 - The field of a moving charge
18 - Radiation by a charge
19 - The radiation reaction force
20 - Interacting charges I
21 - Interacting charges II
22 - Electromagnetism and differential geometry
1 - The equivalence principle
2 - Riemannian manifolds
3 - Matter in curved spacetime
4 - The Einstein equations
5 - Conservation laws
6 - The Schwarzschild solution
7 - The Schwarzschild black hole
8 - The Kerr solution
9 - The physics of black holes I
10 - The physics of black holes II
11 - Tests in the solar system
12 - The post-Newtonian approximation
13 - Gravitational waves and the radiative field
14 - Gravitational radiation
15 - The two-body problem and radiative losses
16 - The two-body problem: an effective-one-body approach
17 - Cosmological spacetimes
18 - Friedmann-Lemaitre spacetimes
19 - The Lambda-CDM model of the hot Big Bang
20 - Inflationary models of the primordial universe
21 - Cosmological perturbations
22 - Primordial quantum perturbations
23 - The covariant derivative and the curvature
24 - Reimannian manifolds
25 - The Cartan structure equations

Nathalie Deruelle is a researcher in Theoretical Physics and Director Research at the CNRS (Centre National de la Recherche Scientifique) in France. She is based at Laboratoire Astroparticules & Cosmologie (APC) at Université Paris VII (Denis-Diderot) and is affiliated professor at the Kyoto Yukawa Institute. Deruelle has lectured at numerous summer schools and universities, including the École Polytechnique and the École Normale Supérieure. Jean-Philippe Uzan is a researcher in Theoretical Physics and Director of Research at the CNRS (Centre National de la Recherche Scientifique) in France. He is currently member of the Institut d'Astrophysique de Paris (IAP) at Université Paris VI (Sorbonne Université). Uzan has taught at several Paris universities, including the École Normale Supérieure, and has published specialized and popular books in physics and cosmology.