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On successful completion of the module, students should be able to:
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Describe the geometry of curved spaces and curved space-times in terms of a metric; derive the Levi-Civita connection associated with a given metric; obtain the Riemann curvature tensor, the Ricci tensor, the Ricci scalar and the Einstein tensor associated with such a metric
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Obtain the geodesic equations in arbitrary space-times
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Derive the Schwarzschild solution to the vacuum Einstein field equations under the assumption of time translational and spherical symmetry
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Derive expressions for the gravitational redshift, the precession of the perihelion of planetary orbits, and the deflection of light rays in the Schwarzschild geometry
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Show that there exist plane-wave solutions to the vacuum Einstein equations in the linear approximation, corresponding to gravational waves, and derive some of their physical properties
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Obtain the energy-momentum tensor for a fluid, discuss the consequences of spatial isotropy for a Universe with a cosmological constant filled with a fluid, and hence construct the Friedmann-Robertson-Walker metric
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Obtain the Friedmann equations from the Einstein field equations, solve these equations for the scale factor and discuss the implications of these solutions
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Describe the evolution of the Universe from the Big Bang, from the first three minutes to the era of star and galaxy formation; explain the origin of low mass chemical elements in the early Universe.
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