Gravitational Waves
A rigorous graduate-level course on gravitational waves — from linearized gravity and wave solutions through the quadrupole formula, astrophysical sources, detection methods, LIGO/Virgo discoveries, and gravitational wave cosmology — with full derivations, MathJax equations, and Python simulations.
Course Overview
Gravitational waves are ripples in spacetime predicted by Einstein's general relativity (1916) and first directly detected by LIGO (2015). These disturbances propagate at the speed of light, carrying information about the most violent events in the universe: colliding black holes, merging neutron stars, supernovae, and the Big Bang itself. This course derives every key result from first principles, following the tradition of Maggiore, Creighton & Anderson, and Schutz.
What You Will Learn
- ● Linearized gravity: metric perturbations and gauge freedom
- ● Plane waves: TT gauge, plus and cross polarizations
- ● Geodesic deviation and interferometric detection
- ● Quadrupole formula: GW generation from accelerated masses
- ● Astrophysical sources: BBH, BNS, pulsars, stochastic
- ● Detection: LIGO, Virgo, KAGRA, LISA, pulsar timing
- ● GW cosmology: standard sirens, modified gravity tests
Central Equations
Wave Equation: $\Box \bar{h}_{\mu\nu} = -\frac{16\pi G}{c^4}T_{\mu\nu}$
TT Gauge: $h^{TT}_{0\mu} = 0$, $h^{TT}_{ii} = 0$, $\partial^j h^{TT}_{ij} = 0$
Strain: $\frac{\Delta L}{L} = \frac{1}{2}h(t)$
Quadrupole: $h_{ij} = \frac{2G}{c^4 r}\ddot{Q}_{ij}^{TT}$
Power: $P = \frac{G}{5c^5}\langle\dddot{Q}_{ij}\dddot{Q}^{ij}\rangle$
Chirp: $\dot{f} = \frac{96}{5}\pi^{8/3}\left(\frac{GM_c}{c^3}\right)^{5/3}f^{11/3}$
Standard Siren: $H_0 = cz/d_L$
1. Linearized Gravity
Metric perturbations, trace-reversal, Lorenz gauge, vacuum wave equation.
2. Plane Waves & Polarizations
TT gauge, plus and cross modes, helicity-2, Newman-Penrose scalars.
3. Effect on Test Masses
Geodesic deviation, proper distance, strain, ring of particles.
4. Quadrupole Formula
Quadrupole moment, radiated power, binary systems, chirp mass.
5. Astrophysical Sources
BBH, BNS, supernovae, continuous waves, stochastic background.
6. Detection Methods
Laser interferometry, LIGO/Virgo/KAGRA, LISA, pulsar timing arrays.
7. Major Detections
GW150914, GW170817, GWTC catalogs, multi-messenger astronomy.
8. GW Cosmology
Standard sirens, Hubble constant, modified gravity, primordial GWs.
9. Future Prospects
Einstein Telescope, Cosmic Explorer, LISA, next-gen science goals.
Research Seminars
Cutting-edge research talks on gravitational wave physics from leading researchers.
QFT Tools for Precision GW Physics
Enrico Hermann
Decoding Biographies of Binary Compact Objects
Isobel Romero-Shaw
Detecting GWs with Binary Resonances
Joshua Foster
Probing Gravity with Gravitational Waves
Maximiliano Isi
Prerequisites & References
Prerequisites
• Fourier analysis and signal processing (helpful)
Recommended Texts
- • Maggiore, Gravitational Waves: Theory and Experiments (2 vols)
- • Creighton & Anderson, Gravitational-Wave Physics and Astronomy
- • Schutz, A First Course in General Relativity
- • Flanagan & Hughes, The Basics of Gravitational Wave Theory (review)
- • Sathyaprakash & Schutz, Physics, Astrophysics and Cosmology with GWs