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General relativity and cosmology course
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Module 4
Schwarzschild Black Holes and Classic Tests of GR
1
Deriving the Schwarzschild Metric
Derive the Schwarzschild metric as the unique static, spherically symmetric vacuum solution (Birkhoff's theorem).
2
Schwarzschild Spacetime: Horizons and Singularities
Analyze the causal structure of Schwarzschild spacetime, identifying the event horizon and physical singularity.
3
Orbits and Light Rays in Schwarzschild Spacetime
Analyze null and timelike geodesics in the Schwarzschild metric to describe particle orbits and light rays.
4
Mercury's Precession: Geodesic Equations in Action
Calculate the perihelion precession of Mercury using the derived geodesic equations.
5
Gravitational Lensing: Deflection of Light
Calculate the deflection of light by a massive object (gravitational lensing).
6
Taming the Event Horizon: Kruskal-Szekeres Coordinates
Analyze the coordinate singularity at the event horizon and remove it using Kruskal-Szekeres coordinates.
7
Penrose Diagram of Maximally Extended Schwarzschild Spacetime
Construct the Penrose diagram for the maximally extended Schwarzschild spacetime.
8
Deriving the Reissner-Nordström Metric
Derive the Reissner-Nordström metric for a charged, non-rotating black hole.
Previous module
The Principles of General Relativity
Next module
Rotating Black Holes and Causal Structure