by Alessandra Buonanno
Publisher: arXiv 2007
Number of pages: 50
Gravitational-wave (GW) science has entered a new era. Theoretically, the last years have been characterized by numerous major advances. These lectures are envisioned to be an introductory, basic course in gravitational-wave physics.
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by Stefan Waner
Smooth manifolds and scalar fields, tangent vectors, contravariant and covariant vector fields, tensor fields, Riemannian manifolds, locally Minkowskian manifolds, covariant differentiation, the Riemann curvature tensor, premises of general relativity.
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Course notes for an introduction to Riemannian geometry and its principal physical application, Einstein’s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus.
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Lecture notes on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications: gravitational radiation, black holes, and cosmology.
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The author presents the pedagogical introduction to relativistic astrophysics and cosmology, which is based on computational and graphical resources of Maple 6. The knowledge of basics of general relativity and differential geometry is supposed.