Lectures on Gravitation

The following sections are included:

• Preface

• Contents

The following sections are included:

• Two dimensional geometry

• Inertial and gravitational masses

• Relativity

The following sections are included:

• Relativistic point particle

• Current and charge densities

• Maxwell's equations in the presence of sources

• Motion of a charged particle in EM field

• Energy-momentum tensor

• Angular momentum

The following sections are included:

• Principle of equivalence

• Principle of general covariance

• Tensor densities

The following sections are included:

• Parallel transport of a vector

• Christoffel symbol

• Covariant derivative of contravariant tensors

• Metric compatibility

• Covariant derivative of covariant and mixed tensors

• Electromagnetic analogy

• Gradient, divergence and curl

The following sections are included:

• Covariant differentiation along a curve

• Curvature from derivatives

• Parallel transport along a closed curve

• Geodesic equation

• Derivation of geodesic equation from a Lagrangian

The following sections are included:

• Geodesic as representing gravitational effect

• Rotating coordinate system and the Coriolis force

• Gravitational red shift

• Twin paradox and general covariance

• Other equations in the presence of gravitation

The following sections are included:

• Curvilinear coordinates versus gravitational field

• Definition of an inertial coordinate frame

• Geodesic deviation

• Properties of the curvature tensor

• Einstein's equation

• Cosmological constant

• Initial value problem

• Einstein's equation from an action

The following sections are included:

• Line element

• Connection

• Solution of the Einstein equation

• Properties of the Schwarzschild solution

• Isotropic coordinates

The following sections are included:

• Radar echo experiment

• Motion of a particle in a Schwarzschild background
  • Vertical free fall
  • Circular orbit

• Motion of light rays in a Schwarzschild background

• Perihelion advance of Mercury

The following sections are included:

• Singularities of the metric

• Singularities of the Schwarzschild metric

• Black holes

The following sections are included:

• Homogeneity and isotropy

• Different models of the universe
  • Close universe
  • Flat universe
  • Open universe

• Hubble's law

• Evolution equation
  • k = 1
  • k = 0
  • k = −1

• Big bang theory and blackbody radiation

The following sections are included:

• Index