Gravitation

"This book suitable for post graduates in Physics and Astrophysics aims at introducing the theory of general relativity as an important background for doing astrophysics. Starting from a detailed discussion of the various mathematical concepts for doing general relativity, the book introduces the geometric description of gravity. It gives a brief historical perspective to classical mechanics and electrodynamics making an attempt to establish the necessity of special relativity as propounded by Einstein extending to General Relativity. This book is a good starting point for post graduates wanting to pursue the modern topics of Cosmology, High energy astrophysics and related areas."-- Read more... Abstract: "This book suitable for post graduates in Physics and Astrophysics aims at introducing the theory of general relativity as an important background for doing astrophysics. Starting from a detailed discussion of the various mathematical concepts for doing general relativity, the book introduces the geometric description of gravity. It gives a brief historical perspective to classical mechanics and electrodynamics making an attempt to establish the necessity of special relativity as propounded by Einstein extending to General Relativity. This book is a good starting point for post graduates wanting to pursue the modern topics of Cosmology, High energy astrophysics and related areas." Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- List of Figures -- List of Tables -- Foreword -- Preface -- 1: Mathematical Preliminaries -- 1.1 Introduction -- 1.1.1 Vectors, differential forms and tensors -- 1.1.1.1 Vector algebra and calculus -- 1.1.2 Covectors and Differential forms -- 1.1.2.1 Algebra and calculus of forms -- 1.1.2.2 Exterior differentiation -- 1.1.2.3 Mapping of forms -- 1.1.3 Tensors -- 1.1.3.1 Tensor algebra -- 1.2 Groups -- 1.3 Variational calculus -- 1.3.0.1 The brachistrochrone -- 1.4 Geometry -- 1.4.1 Introduction -- 1.4.2 Conic sections -- 1.4.2.1 Ellipse -- 1.4.2.2 Parabola -- 1.4.2.3 Hyperbola -- 1.4.3 Metric, connection and curvature -- 1.4.3.1 Curvature -- Bibliography -- 2: Prerelativity Physics -- 2.1 Classical mechanics -- 2.1.1 Introduction -- 2.1.2 Concept of inertia and laws of motion -- 2.1.3 Particle mechanics -- 2.1.3.1 Momentum -- 2.1.4 Kepler's laws of planetary motion -- 2.1.4.1 Velocity and acceleration in polar coordinates -- 2.1.4.2 Projectile motion -- 2.1.4.3 Energy -- 2.1.4.4 System of particles -- 2.1.5 Lagrangian mechanics -- 2.1.5.1 Euler-Lagrange equations -- 2.1.6 Symmetry and conservation laws -- 2.1.6.1 Effective potential -- 2.2 Optics and electrodynamics -- 2.2.1 Introduction -- 2.2.2 Light-Its speed and nature -- 2.2.2.1 Michelson-Morley experiment -- 2.2.3 Electromagnetism -- 2.2.3.1 Maxwell's equations -- 2.2.3.2 Wave equation -- 2.3 Plasma physics and fluid dynamics -- 2.3.1 Introduction -- 2.3.2 Fluid dynamics -- 2.3.2.1 Equations of motion -- 2.3.2.2 Equations of state -- 2.3.2.3 Integration of Euler's equations -- 2.3.2.4 General fluids -- 2.3.2.5 Viscous fluids -- 2.3.2.6 Rayleigh criterion -- 2.3.3 Plasma physics -- 2.3.3.1 Single particle approach and guiding center approximation -- 2.3.4 Magnetohydrodynamics -- Bibliography "This book suitable for post graduates in Physics and Astrophysics aims at introducing the theory of general relativity as an important background for doing astrophysics. Starting from a detailed discussion of the various mathematical concepts for doing general relativity, the book introduces the geometric description of gravity. It gives a brief historical perspective to classical mechanics and electrodynamics making an attempt to establish the necessity of special relativity as propounded by Einstein extending to General Relativity. This book is a good starting point for post graduates wanting to pursue the modern topics of Cosmology, High energy astrophysics and related areas."-- Résumé de l'éditeur Content: Mathematical Preliminaries. Pre Relativistic Physics. Special Relativity. General Relativity. Accretion Astrophysics. Inertial Forces in GR. Gravity as a Gauge Theory.