General Relativity - U02 Lecture The Metric

The Metric

. The Metric and the additional structure that it endows on a differentiable manifold
. Abstract index notation
. Definition - Pseudo-Riemannian metrics
. Index raising/lowering
. Orthonormal bases - local observers
. Local inertial frames and freely falling observers
. Local light cone and causal structure
. Global causal structure (overview+definitions)
. Examples: Misner space+closed timelike curves, wormhole geometry, flat-space cosmology

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Supplementary material for the undergraduate course “General Relativity and Cosmology” offered at the Physics Department of the School of Applied Mathematical and Physical Sciences of the National Technical University of Athens (NTUA).

Instructor:
Konstantinos N. Anagnostopoulos (spring 2023), Associate Professor of Physics, NTUA