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Relativity and Cosmology By Muhammad Bani Amin pdf Book free Download

Admin July 03, 2024

 


Relativity and Cosmology By Muhammad Bani Amin pdf Book free Download


CONTENTS

Introduction

1. Special Theory of Relativity

1.1 Review of previous concepts

  • Frame of Reference
  • Inertial frame of reference
  • Non-inertial frame of reference
  • Observer

1.2 Michelson-Morley experiment 1.3 Einstein paradox 1.4 Newtonian Framework

1.4.1 Galilean relativity

  • Transformation of length
  • Transformation of velocity
  • Transformation of acceleration
  • Transformation of force
  • Galilean principle of relativity

1.5 Einstein's postulates of special relativity 1.6 Radar method 1.7 Bondi k-calcul

  • Relative speed of two inertial observers
  • Multiple Reflections

1.8 Interval 1.9 Composition law for velocities

  • Derivation of Newtonian velocity composition law
  • Constancy of the speed of light postulate
  • Types of particles on basis of special relativity

1.10 Structure of space-time 1.11 Light cone 1.12 Lorentz transformations

  • Derivation of Lorentz transformations from postulates of special relativity
  • Derivation of Lorentz transformations from rotation of coordinate axes
  • Special Lorentz transformation
  • Deduction of Galilean transformations from Lorentz transformations

1.13 Consequences of Lorentz transformations

  • Relativity of simultaneity
  • Length contraction
  • Time dilation
  • Twin paradox
  • Doppler Effect
  • Classical Doppler Effect
  • Pseudo velocity

1.15 Transformation law for velocities

  • Law of addition of velocities 1.15.1 Lorentz transformation law for direction cosines 1.16 Transformation law for acceleration 1.17 Minkowski space-time tensors
  • 4-vector
  • Lorentz tensor
  • Metric tensor

For your understanding:

  • Questions with answers
  • Multiple Choice Questions

Test your understanding:

  • Review Questions
  • Problems
  • Review Problems
  1. Relativistic Mechanics

2.1 Force equation in relativity 2.2 Variation of mass with velocity 2.3 4-velocity 2.4 4-acceleration 2.5 4-force 2.6 Momentum-energy relation 2.7 Momentum of photon 2.8 Kinetic energy of a particle 2.9 Total energy of a particle 2.10 Transformation of energy and momentum 2.11 Relativistic Electrodynamics 2.12 Equation of continuity 2.13 4-vector potential 2.14 Lorentz potential and field strength tensor 2.15 Covariant form of Maxwell equations 2.16 Compton scattering

For your understanding:

  • Questions with answers
  • More Solved Examples
  • Multiple Choice Questions

Test your understanding:

  • Review Questions
  • Exercises
  • Problems
  • Review Problems
  1. Elements of Tensor Calculus

3.1 Tensors

Types of tensors

  • Covariant tensors
  • Contra-variant tensors

3.1.1 Symmetry and anti-symmetry of tensors

  • Kronecker delta symbol

3.1.3 Levi Civita tensor 3.2 Tensor algebra

  • Addition and subtraction of tensors
  • Interchange of indices
  • Invariant tensors (scalars)
  • Rank of a tensor
  • Outer product
  • Contracted tensor
  • Inner product
  • Trace of a matrix

3.2.1 Quotient law 3.3 Manifolds and coordinates

  • Coordinate patches
  • Atlas
  • Importance of manifold

3.3.1 Curves and surfaces 3.3.2 Coordinate transformation 3.3.3 Tensor fields

  • Tangent Space
  • Covariant differentiation of tensor field

3.4 4-dimensional space-time

  • Metric tensor
  • Riemann space

3.5 Intrinsic curvature of a metric 3.7 Associated tensors 3.7.1 Scalar product 3.7.2 Vector product 3.8 Christoffel symbols 3.9 Geodesic equation 3.10 Riemann curvature tensor 3.1.1 Partial derivative 3.12 Covariant derivative 3.13 Lie derivative 3.13.1 Bianchi identities 3.14 Ricci tensor 3.15 Einstein tensor and its derivations

For your understanding:

  • Questions with answers
  • More Solved Examples
  • Multiple Choice Questions

Test your understanding:

  1. General Relativity and Cosmology

4.1 Principles of general relativity 4.1.2 Principle of equivalence

  • Newtonian form of principle of equivalence
  • Relativistic form of principle of equivalence
  • Mass in Newtonian mechanics
  • Mass in general principle of equivalence
  • Weak and strong principle of equivalence

4.1.3 The principle of covariance 4.1.4 Principle of minimal gravitational coupling

4.2 Einstein's field equations 4.2.1 Newton and Einstein on mutual gravity 4.2.2 Poisson equation for gravitational potential 4.2.3 Equation of geodesics deviation 4.3 Tests of general relativity theory

  • Perihelion of the orbit of Mercury
  • Bending of light rays in a gravitational field
  • Radar echo delay

4.4 Newtonian metric 4.5 Friedmann-Robertson-Walker metric 4.7 Schwarzschild metric 4.8 Black holes

  • Formation of black holes
  • Conditions for formation of stars and black holes
  • Detection of black holes

4.9 Hubble’s law

  • Hubble time and radius
  • Derivation of Hubble's law from the Friedmann-Robertson-Walker metric
  • Hubble parameter

4.9.1 Achievements of Hubble's law 4.9.2 Limitations of Hubble's law 4.10 Cosmological principle 4.11 Astrophysical models


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