gwbinaries_florence_2026

Gravitational waves from compact binaries

Davide Gerosa - davide.gerosa@unimib.it
Caroline Owen - caroline.owen@unimib.it

University of Milano-Bicocca, 2026.

Aims

This is a PhD-level class on “Gravitational waves from compact binaries” of about 10 hours. We cover the principles of gravitational-wave propagation and emission, from the linearized Einstein equations to the quadrupole formula. This formalism is then applied to the specific case of binary black holes, including their dynamics on eccentric orbits and gravitational-wave propagation on cosmological backgrounds. We then cover the theory behind gravitational-wave detectors with laser interferometers.

Florence 2026

We prepared this material for a PhD course we’re teaching at the PhD school Theoretical Aspects of Astroparticle Physics, Cosmology and Gravitation, which will take place at the Galileo Galilei Institute for Theoretical Physics in Florence in March 2026. Lectures by Davide Gerosa, example classes by Caroline Owen.

Prerequisites

This class assumes students have already seen and understood (well, that’s a big word!) General Relativity at the graduate level, including general knowledge of tensor and vector calculus.

I mostly follow Maggiore’s textbook (“Gravitational waves, Volume 1: theory and experiments“). Indeed, numbering of sections and equations in Davide’s notes refer to Maggiore’s book.

Lecture notes (Davide Gerosa)

  1. GW propagation. Linearized gravity. Energy of GWs. Background vs perturbation. Energy flux.
  2. GW emission. Quadrupolar approximation. Leading-order emission. Radiated energy (quadrupole formula). Radiation reaction.
  3. Binaries (part 1) Fixed circular orbits. Angular pattern. Quasi-circular orbits with backreaction. Inspiral timescale. Chirp signal.
  4. Binaries (part 2) Eccentric orbits. Peters equations. Orbit circularization. Propagation in cosmological background. Redshifted mass.
  5. GW detection Interaction with GW - test masses. TT frame. Laboratory frame. Detector response. Beam patterns for interferometers.

Example classes (Caroline Owen)

  1. Dimensional analysis and Fermi estimates
  2. Stationary phase approximation
  3. Bilby tutorial

Careful…

Credit: what-if.xkcd.com/140