Øyvind Grøn
Lecture Notes on the General Theory of Relativity (eBook, PDF)
From Newton’s Attractive Gravity to the Repulsive Gravity of Vacuum Energy
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Øyvind Grøn
Lecture Notes on the General Theory of Relativity (eBook, PDF)
From Newton’s Attractive Gravity to the Repulsive Gravity of Vacuum Energy
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This book collects lectures on the general theory of relativity given by Dr. Øyvind Grøn at the University of Oslo, Norway. This accessible text allows students to follow the deductions all the way throughout the book.
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This book collects lectures on the general theory of relativity given by Dr. Øyvind Grøn at the University of Oslo, Norway. This accessible text allows students to follow the deductions all the way throughout the book.
Produktdetails
- Produktdetails
- Verlag: Springer / Springer New York
- Erscheinungstermin: 23. März 2010
- Englisch
- ISBN-13: 9780387881348
- Artikelnr.: 43796416
- Verlag: Springer / Springer New York
- Erscheinungstermin: 23. März 2010
- Englisch
- ISBN-13: 9780387881348
- Artikelnr.: 43796416
Newton’s law of universal gravitation.- The force law of gravitation.- Newton’s law of gravitation in local form.- Tidal forces.- The principle of equivalence.- The general principle of relativity.- The covariance principle.- Mach’s principle.- The special theory of relativity.- Coordinate systems and Minkowski diagrams.- Synchronization of clocks.- The Doppler effect.- Relativistic time-dilation.- The relativity of simultaneity.- The Lorentz contraction.- The Lorentz transformation.- The Lorentz invariant interval.- The twin paradox.- Hyperbolic motion.- Energy and mass.- Relativistic increase of mass.- Tachyons.- Magnetism as a relativistic second order effect.- Vectors, tensors and forms.- Vectors.- Four-vectors.- Tangent vector fields and coordinate vectors.- Coordinate transformations.- Structure coefficients.- Tensors.- Transformation of tensor components.- Transformation of basis 1-forms.- The metric tensor.- Forms.- Rotating and accelerated reference frames.- Rotating reference frames.- The spatial metric tensor.- Angular acceleration of the rotating frame.- Gravitational time dilation.- Path of photons emitted from the axis in a rotating frame.- The Sagnac effect.- Uniformly accelerated reference frames.- Covariant differentiation.- Differentiation of forms.- Exterior differentiation.- Covariant derivative.- The Christoffel symbols.- Geodetic curves.- The covariant Euler-Lagrange equations.- Application of the Lagrange formalism to free particles.- Equation of motion from Lagrange’s equations.- Geodesic worldliness in spacetime.- Gravitational Doppler effect.- The Koszul connection.- Connection coefficients and structure coefficients in a Riemannian (torsion free) space.- Covariant differentiation of vectors, forms and tensors.- Covariant differentiation of a vector field in an arbitrary basis.- Covariant differentiation of forms.- Generalization for tensors of higher rank.- The Cartan connection.- Curvature.- The Riemann curvature tensor.- Differential geometry of surfaces.- Surface curvature using the Cartan formalism.- The Ricci identity.- Bianchi’s 1st identity.- Bianchi’s 2nd identity.- Einstein’s field equations.- Energy-momentum conservation.- Newtonian fluid.- Perfect fluids.- Einstein’s curvature tensor.- Einstein’s field equations.- The 'geodesic postulate' as a consequence of the field equations.- The Schwarschild spacetime.- Schwarzschild’s exterior solution.- Radial free fall in Schwarzschild spacetime.- Light cones in Schwarzschild spacetime.- Analytical extension of the Schwarzschild coordinates.- Embedding of the Schwarzschild metric.- Deceleration of light.- Particle trajectories in Schwarzschild 3-space.- Motion in the equatorial plane.- Classical tests of Einstein’s general theory of relativity.- The Hafele-Keating experiment.- Mercury’s perihelion precession.- Deflection of light.- Black holes.- 'Surface gravity': gravitational acceleration on the horizon of a black hole.- Hawking radiation: radiation from a black hole.- Rotating black holes: The Kerr metric.- Zero-angular-momentum-observers.- Does the Kerr space have a horizon?.- Schwarzschild’s interior solution.- Newtonian incompressible star.- The pressure contribution to the gravitational mass of a static, spherically symmetric system.- The Tolman-Oppenheimer-Volkov equation.- An exact solution for incompressible stars – Schwarzschild’s interior solution.- Cosmology.- Comoving coordinate system.- Curvature isotropy – the Robertson-Walker metric.- Cosmic dynamics.- Hubble’s law.- Cosmological redshift of light.- Cosmic fluids.- Isotropic and homogeneous universe models.- Some cosmological models.- Radiation dominated model.- Dust dominated model.- Transition from radiation to matter dominated universe.- Friegmann-Lemaître model.- Inflationary cosmology.- Problems with the Big Bang models.- Cosmic inflation.
Newton's Law of Universal Gravitation.- The Special Theory of Relativity.- Vectors, Tensors and Forms.- Accelerated Reference Frames.- Covariant Differentiation.- Curvature.- Einstein's Field Equations.- The Schwarzschild Spacetime.- Black Holes.- Schwarzschild's Interior Solution.- Cosmology.
Newton’s law of universal gravitation.- The force law of gravitation.- Newton’s law of gravitation in local form.- Tidal forces.- The principle of equivalence.- The general principle of relativity.- The covariance principle.- Mach’s principle.- The special theory of relativity.- Coordinate systems and Minkowski diagrams.- Synchronization of clocks.- The Doppler effect.- Relativistic time-dilation.- The relativity of simultaneity.- The Lorentz contraction.- The Lorentz transformation.- The Lorentz invariant interval.- The twin paradox.- Hyperbolic motion.- Energy and mass.- Relativistic increase of mass.- Tachyons.- Magnetism as a relativistic second order effect.- Vectors, tensors and forms.- Vectors.- Four-vectors.- Tangent vector fields and coordinate vectors.- Coordinate transformations.- Structure coefficients.- Tensors.- Transformation of tensor components.- Transformation of basis 1-forms.- The metric tensor.- Forms.- Rotating and accelerated reference frames.- Rotating reference frames.- The spatial metric tensor.- Angular acceleration of the rotating frame.- Gravitational time dilation.- Path of photons emitted from the axis in a rotating frame.- The Sagnac effect.- Uniformly accelerated reference frames.- Covariant differentiation.- Differentiation of forms.- Exterior differentiation.- Covariant derivative.- The Christoffel symbols.- Geodetic curves.- The covariant Euler-Lagrange equations.- Application of the Lagrange formalism to free particles.- Equation of motion from Lagrange’s equations.- Geodesic worldliness in spacetime.- Gravitational Doppler effect.- The Koszul connection.- Connection coefficients and structure coefficients in a Riemannian (torsion free) space.- Covariant differentiation of vectors, forms and tensors.- Covariant differentiation of a vector field in an arbitrary basis.- Covariant differentiation of forms.- Generalization for tensors of higher rank.- The Cartan connection.- Curvature.- The Riemann curvature tensor.- Differential geometry of surfaces.- Surface curvature using the Cartan formalism.- The Ricci identity.- Bianchi’s 1st identity.- Bianchi’s 2nd identity.- Einstein’s field equations.- Energy-momentum conservation.- Newtonian fluid.- Perfect fluids.- Einstein’s curvature tensor.- Einstein’s field equations.- The 'geodesic postulate' as a consequence of the field equations.- The Schwarschild spacetime.- Schwarzschild’s exterior solution.- Radial free fall in Schwarzschild spacetime.- Light cones in Schwarzschild spacetime.- Analytical extension of the Schwarzschild coordinates.- Embedding of the Schwarzschild metric.- Deceleration of light.- Particle trajectories in Schwarzschild 3-space.- Motion in the equatorial plane.- Classical tests of Einstein’s general theory of relativity.- The Hafele-Keating experiment.- Mercury’s perihelion precession.- Deflection of light.- Black holes.- 'Surface gravity': gravitational acceleration on the horizon of a black hole.- Hawking radiation: radiation from a black hole.- Rotating black holes: The Kerr metric.- Zero-angular-momentum-observers.- Does the Kerr space have a horizon?.- Schwarzschild’s interior solution.- Newtonian incompressible star.- The pressure contribution to the gravitational mass of a static, spherically symmetric system.- The Tolman-Oppenheimer-Volkov equation.- An exact solution for incompressible stars – Schwarzschild’s interior solution.- Cosmology.- Comoving coordinate system.- Curvature isotropy – the Robertson-Walker metric.- Cosmic dynamics.- Hubble’s law.- Cosmological redshift of light.- Cosmic fluids.- Isotropic and homogeneous universe models.- Some cosmological models.- Radiation dominated model.- Dust dominated model.- Transition from radiation to matter dominated universe.- Friegmann-Lemaître model.- Inflationary cosmology.- Problems with the Big Bang models.- Cosmic inflation.
Newton's Law of Universal Gravitation.- The Special Theory of Relativity.- Vectors, Tensors and Forms.- Accelerated Reference Frames.- Covariant Differentiation.- Curvature.- Einstein's Field Equations.- The Schwarzschild Spacetime.- Black Holes.- Schwarzschild's Interior Solution.- Cosmology.
From the reviews:
"The textbook is self-contained and designed for master students. The book provides an introduction to abstract notations for tensor calculus and differential geometry, in particular the calculus of differential forms." (Vladimir Dzhunushaliev, Zentralblatt MATH, Vol. 1192, 2010)
"This book collects the lecture notes of a course on general relativity ... . The text is enriched by a collection of interesting and stimulating exercises, which both allow a working knowledge of the theory and provide further insight into the theory itself and its applications as well. Together with the personal didactical approach taken by the author in his book, these exercises may represent useful hints for a teacher wishing to introduce new ideas in a standard introductory course on general relativity." (Giovanni Preti, Mathematical Reviews, Issue 2011 k)
"The textbook is self-contained and designed for master students. The book provides an introduction to abstract notations for tensor calculus and differential geometry, in particular the calculus of differential forms." (Vladimir Dzhunushaliev, Zentralblatt MATH, Vol. 1192, 2010)
"This book collects the lecture notes of a course on general relativity ... . The text is enriched by a collection of interesting and stimulating exercises, which both allow a working knowledge of the theory and provide further insight into the theory itself and its applications as well. Together with the personal didactical approach taken by the author in his book, these exercises may represent useful hints for a teacher wishing to introduce new ideas in a standard introductory course on general relativity." (Giovanni Preti, Mathematical Reviews, Issue 2011 k)