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A College Course on Relativity and Cosmology /
This advanced undergraduate text introduces Einstein's general theory of relativity. The topics covered include geometric formulation of special relativity, the principle of equivalence, Einstein's field equation and its spherical-symmetric solution, as well as cosmology. An emphasis is pl...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Oxford University Press USA,
2015.
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| Edición: | First edition. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Preface; Contents; 1 Introduction; 1.1 Relativity as a coordinate symmetry; 1.1.1 Coordinate transformations; 1.1.2 The principle of relativity; 1.2 Einstein and relativity; 1.2.1 The new kinematics; 1.2.2 GR as a field theory of gravitation; Review questions; 2 Special Relativity: The New Kinematics; 2.1 Einstein's two postulates and Lorentz transformation; 2.1.1 Relativity of simultaneity and the new conception of time; 2.1.2 Coordinate-dependent time leads to Lorentz transformation; 2.2 Physics implications of Lorentz transformation; 2.2.1 Time dilation and length contraction.
- 2.2.2 The invariant interval and proper time2.3 Two counterintuitive scenarios as paradoxes; Review questions; 3 Special Relativity: Flat Spacetime; 3.1 Geometric formulation of relativity; 3.2 Tensors in special relativity; 3.2.1 Generalized coordinates: bases and the metric; 3.2.2 Velocity and momentum 4-vectors; 3.2.3 Electromagnetic field 4-tensor; 3.2.4 The energy-momentum-stress 4-tensor for a field system; 3.3 The spacetime diagram; 3.3.1 Invariant regions and causal structure; 3.3.2 Lorentz transformation in the spacetime diagram; Review questions.
- 4 Equivalence of Gravitation and Inertia4.1 Seeking a relativistic theory of gravitation; 4.1.1 Newtonian potential: a summary; 4.1.2 Einstein's motivation for general relativity; 4.2 The equivalence principle: from Galileo to Einstein; 4.2.1 Inertial mass vs. gravitational mass; 4.2.2 Einstein: ''my happiest thought''; 4.3 EP leads to gravitational time dilation and light deflection; 4.3.1 Gravitational redshift and time dilation; 4.3.2 Relativity and the operation of GPS; 4.3.3 The EP calculation of light deflection; 4.3.4 Energetics of light transmission in a gravitational field.
- Review questions5 General Relativity as a Geometric Theory of Gravity; 5.1 Metric description of a curved manifold; 5.1.1 Gaussian coordinates and the metric tensor; 5.1.2 The geodesic equation; 5.1.3 Local Euclidean frames and the flatness theorem; 5.2 From the equivalence principle to a metric theory of gravity; 5.2.1 Curved spacetime as gravitational field; 5.2.2 GR as a field theory of gravitation; 5.3 Geodesic equation as the GR equation of motion; 5.3.1 The Newtonian limit; Review questions; 6 Einstein Equation and its Spherical Solution; 6.1 Curvature: a short introduction.
- 6.2 Tidal gravity and spacetime curvature6.2.1 Tidal forces-a qualitative discussion; 6.2.2 Deviation equations and tidal gravity; 6.3 The GR field equation; 6.3.1 Einstein curvature tensor; 6.3.2 Einstein field equation; 6.3.3 Gravitational waves; 6.4 Geodesics in Schwarzschild spacetime; 6.4.1 The geometry of a spherically symmetric spacetime; 6.4.2 Curved spacetime and deflection of light; 6.4.3 Precession of Mercury's orbit; Review questions; 7 Black Holes; 7.1 Schwarzschild black holes; 7.1.1 Time measurements around a black hole; 7.1.2 Causal structure of the Schwarzschild surface.