Physics / advanced
Spacetime, gravitation, and cosmology
Develop general relativity from local measurements to curvature, gravitational waves, black holes, and expanding universes.
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Module 01 advanced
Spacetime, gravitation, and cosmology
Develop general relativity from local measurements to curvature, gravitational waves, black holes, and expanding universes.
- 01
Relativistic energy and the stress tensor
Connect four-momentum, local energy measurements, pressure, and the stress tensor that supplies gravity’s matter source.
27 min - 02
The equivalence principle and local frames
Distinguish free fall from supported motion, construct local inertial descriptions, and understand the limits imposed by tidal gravity.
25 min - 03
Metrics and geodesic motion
Read proper time from a metric, derive the geodesic equation, and separate coordinate effects from physical acceleration.
28 min - 04
Curvature and geodesic deviation
Define a curvature convention, relate it to measurable tidal acceleration, and understand why vacuum can still contain gravitational curvature.
29 min - 05
Einstein’s equations and the Newtonian limit
Relate matter to curvature, separate constraints from evolution, and recover Poisson’s equation in a controlled weak-field limit.
30 min - 06
Schwarzschild orbits and perihelion precession
Use a spherical vacuum geometry, conserved geodesic quantities, and a controlled orbital correction to predict perihelion advance.
30 min - 07
Black-hole horizons and causal structure
Separate a coordinate singularity from curvature blow-up, use horizon-regular coordinates, and define an event horizon through causal escape.
29 min - 08
Gravitational waves and detector measurements
Connect weak radiative metric perturbations, transverse tidal strain, interferometer response, and evidence from coherent detector observations.
30 min - 09
Friedmann cosmology and redshift
Use homogeneous expanding geometry, fluid conservation, and scale-factor normalization to connect redshift with matter and radiation evolution.
31 min - 10
Quantum fields in curved spacetime
Separate field quantization on a classical background from quantum gravity, and connect particle ambiguity, detector response, and Hawking temperature.
33 min