Course topics
Preliminary course program (subject to change). Gray text:
planned topics; black text: final topics.| Lesson |
Date |
Topics |
Slides and useful links |
Hours (total) |
| 1 |
1/10/2024 |
Introduction to the course, general
overview of gravitational-wave research. Review of SR and notation. The Ives and Stilwell experiment. The GZK cutoff. |
Handout: Notation and SR topics | 2 |
| 2 |
2/10/2024 | Introduction to General Relativity (1). Riemann manifolds and curved spaces. Tensors. |
|
3 |
| 3 |
3/10/2024 | Introduction to General Relativity (2). More on tensors. |
|
5 |
| 4 |
8/10/2024 | Introduction to General Relativity (3). Tidal forces. The Roche limit. Riemann manifolds and curved spaces - Christoffel symbols, covariant derivative, parallel transport |
Image of Saturn and its ring system. |
7 |
| 5 |
9/10/2024 | Introduction to General Relativity (4). Worked example on the connection coefficients. Geodesic equations. | Handouts: Worked example on the connection coefficients; Geodesic equations. | 8 |
| 6 |
10/10/2024 | Introduction to General Relativity (5). Geodesic equations from the free-particle Lagrangian (ctd.). Equivalence between the two forms of geodesic equations.The Riemann curvature tensor, the Ricci tensor, the Ricci scalar. | Handouts: Geodesic
equations; The Riemann tensor;
Sign conventions. |
10 |
| 7 |
14/10/2024 | Symmetries of the Riemann and of the
Ricci tensors. Number of independent components of the
Riemann and Ricci tensors. Geodesic deviation. Key principles of GR: principle of general covariance; principle of consistency; equivalence principle. |
Handouts: Symmetries
of the Riemann and Ricci tensors; Independent
components or Riemann and Ricci tensors; Geodesic
deviation Paper on the E=mc2 formula, by L. Okun Slides on key principles of GR |
12 |
| 8 |
16/10/2024 | Key principles of GR (ctd.): experimental
tests of the weak equivalence principle. |
Slides
on key principles of GR |
13 |
| 9 |
17/10/2024 |
Introduction to General Relativity (6).
The stress-energy tensor. The Einstein equations. A short history of gravitational waves. |
Handouts: The
stress-energy tensor; Einstein's
equations. Slides on the history of gravitational waves |
15 |
| 10 |
21/10/2024 | A short history of gravitational waves
(ctd.) GWs at the Chapel Hill conference (1957). The Newtonian limit. |
Handout: Newtonian limit Slides on the history of gravitational waves Link to P. Saulson's presentation on Pirani's contribution |
17 |
| 11 |
23/10/2024 | The Newtonian limit (ctd.) |
Handout: Newtonian
limit |
18 |
| 12 |
24/10/2024 |
Linearized gravity; The Lorentz gauge.
Gravitational waves (GW) in GR. The tranverse-traceless
(TT) gauge. Local curvature of space-time and magnitude of the Ricci scalar. |
Handouts: Linearized gravity;
The
TT gauge and the detection of gravitational waves;
Curvature
and magnitude of the Ricci scalar |
20 |
| 13 |
28/10/2024 | Gravitational wave
polarization. Interferometric detection of gravitational waves (1): the Michelson interferometer as basic scheme. LASER beam modulation and sidebands. |
Handouts: The TT gauge and the
detection of gravitational waves; Reflection and
transmission coefficients Slides on the interferometric detection of gravitational waves Marco Kraans' short movie on the working principles of a GW interferometer. Paper introducing GW interferometers |
22 |
| 14 |
30/10/2024 | Interferometric detection of
gravitational waves (2): Schnupp asymmetry;
overview of the Virgo optical technology; |
Slides
on the interferometric detection of gravitational
waves |
23 |
| 15 |
31/10/2024 | Interferometric detection of
gravitational waves (3): fundamentals of Fabry-Perot
resonators; matrix optics;optical stability of
Fabry-Perot resonators |
Slides
on the interferometric detection of gravitational
waves |
25 |
| 16 |
4/11/2024 | Interferometric detection of
gravitational waves (4): transfer function of the
Michelson interferometer with FP arms; power recycling.
Overview of further optical improvements. Generation of gravitational waves. |
Handout: Generation of
gravitational waves Slides on the interferometric detection of gravitational waves |
27 |
| 17 |
11/11/2024 | Generation of gravitational waves (ctd.). Gravitational waves produced by simple configurations of moving masses. Calculation of the Ricci tensor of GWs. The stress-energy tensor of GWs and the energy flux. Compact binary coalescences. | Handouts: Generation of
gravitational waves; GW stress-energy
tensor; The GW stress-energy
tensor in the TT gauge; T.A. Moore's
diagonal metric worksheet |
29 |
| 18 |
13/11/2024 | Total power emitted by a GW source. |
Handouts: Total
emitted GW power |
30 |
| 19 |
14/11/2024 | History of the quadrupole formula.
PSR1913+16. The Newtonian approximation for compact
binary systems. |
Handouts: History of
the quadrupole formula; Compact binary coalescenses
in the Newtonian approximation Slides on PSR1913+16. |
32 |
| 20 |
18/11/2024 | The Newtonian approximation for compact
binary systems (ctd.). The GW150914 detection paper. The physics of the black hole merger GW150914. The post-Newtonian approximation. |
Handouts: Compact
binary coalescences in the Newtonian approximation;
post-Newtonian
approximation The first detection paper. Commentary by E. Berti. Paper on the basic physics of the black hole merger GW150914 + Cover + Chandra page on RX J0806.3+1527 |
34 |
| 21 |
20/11/2024 | Noise sources and sensitivity of
gravitational wave detectors. Introduction to the theory
of thermal noises. |
Handouts: Noise sources | 35 |
| 22 |
21/11/2024 | The Langevin stochastic equation and the
Fluctuation-Dissipation theorem. Application of the
theory of thermal noises to mechanical oscillators. Shot
noise in GW interferometers. Glitches. Antenna patterns. |
Handouts: Noise sources;
Antenna
patterns Links to GravitySpy and GWitchHunters |
37 |
| 23 |
25/11/2024 | Antenna patterns (ctd.). Exotic sources. Introduction to the analysis of GW signals. Convolution theorem. Wiener-Kintchine theorem. |
Handouts: Antenna
patterns; Exotic sources;
Matched filters |
39 |
| 24 |
27/11/2024 | Matched filters. |
Handouts: Matched filters | 40 |
| 25 |
28/11/2024 | Matched filters (ctd.). Antenna patterns
in the context of GW signal analysis. Excess power
methods. The False Alarm Rate (FAR). Video on Rai Weiss about the early history of GW research |
Handouts: Matched filters;
Excess power
methods; The False Alarm Rate;
Antenna
patterns 2;
Link to the video on Rai Weiss |
42 |
| 26 |
2/12/2024 |
GW sources (1): BBH, BNS, NSBH mergers;
continuous wave sources; generalities on neutron stars. The GW Data Plotter app for a quick view and analysis of public GW events (presentation by Prof. Agata Trovato) |
Slides
on GW sources Link to GW Data Plotter. Link to the GWOSC (Gravitational Wave Open Science Center) website. |
44 |
| 27 |
5/12/2024 |
GW sources (2): Neutron stars;
core-collapse supernovae (CCSN).GW sources (ctd.): more
on CCSNs; the stochastic GW backround. Coalescences of
neutron star binaries and kilonova events. The first BNS
event: GW170817 and the birth of multimessenger
astronomy with gravitational waves. |
Handouts: Note on
the Li and Paczinski paper. Link to the paper by Li and Paczinski. Slides on GW sources Slides on GW170817 |
46 |
| 28 |
9/12/2024 |
The Schwarzschild metric. Birkhoff's
theorem. Facts about black holes. The near- and medium-term future of GW astrophysics. |
Handouts: The Schwarzschild
metric and associated phenomena. Slides about BHs Slides about the future of GW science Science summary populations of compact objects observed by LVK |
48 |
