(in Polish) Wave propagation in curved spacetimes 1100-WPCS

1. Wave equations in GR
- scalar wave equation
- electromagnetic wave equation
- gravitational wave equation
- waves in Minkowski, waves in curved spacetimes

2. Geometrical optics approximation
- eikonal approximation
- null geodesic equation, transport of polarization tensor
- limitations
- properties: time of arrival, multiple images etc.
- energy flux
- SR effects: relativistic light beaming, red/blueshift, aberration effect
- conformal invariance of null geodesics. Light in FRLW spacetime.

3. Theory of infinitesimal light bundles
- geodesic deviation equation of the 1st order: timelike, null
- resolvent, Jacobi matrix, etc.
- momentary measurements. Flux, angular diameter distance, luminosity distiance
- drifts, parallax etc.
- world-function formalism (perhaps)
- light bundles, Raychaudhuri equation

4. Lensing theory
- light rays in Newtonian approximation, gravitational light bending formula
- lensing in thin lens approximation: lensing equation
- Fermat principle, TOA
- lensing in FLRW spacetime
- conservation of flux, light intensity
- moving lens - perhaps?
- caustics
- beyond the thin lens approximation
- Schwarzschild BH: photonsphere, BH shadow
- Kerr: photonsphere, BH shadow
- multiple images

5. Focus on gravitational waves
- gauge, polarization
- energy flux
- source: quadrupole formula
- BBH signal
- detection: TOA of electromagntetic waves
- interferometers
- PTA's
- memory effect

6. Wave effects
- beyond the 0th order eikonal equation
- spin-Hall effect
- Fresnel formula?
- waves in Schwarzschild, quasinormal modes?
- superradiance?