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 |
3/10/2023 |
Introduction to the course, general
overview of gravitational-wave research. (1) |
1 |
|
| 2 |
5/10/2023 | Introduction to the course, general
overview of gravitational-wave research. (2) Review of SR and notation. The Ives and Stilwell experiment. |
|
3 |
| 3 |
9/10/2023 | Introduction to General Relativity (1).
Riemann manifolds and curved spaces - 1. Tensors. |
|
5 |
| 4 |
12/10/2023 | Introduction to General Relativity (2).
Riemann manifolds and curved spaces - More on tensors. |
|
7 |
| 5 |
16/10/2023 | Introduction to General Relativity (3).
Riemann manifolds and curved spaces - Christoffel
symbols, covariant derivative, parallel transport,
geodesic equations. Geodesic equations from the
free-particle Lagrangian. Equivalence between the two
forms of geodesic equations. |
Handouts: Riemann
manifolds; Geodesic equations
|
9 |
| 6 |
19/10/2023 | Introduction to General Relativity (4).
The Riemann curvature tensor, the Ricci tensor, the
Ricci scalar. |
Handout: The Riemann
tensor |
11 |
| 7 |
23/10/2023 | Introduction to General Relativity (5).
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; experimental tests of the weak equivalence principle. |
Handouts:
Symmetries of the Riemann and Ricci tensors; Independent
components or Riemann and Ricci tensors; Geodesic
deviation Slides on key principles of GR |
13 |
| 8 |
26/10/2023 | 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 |
15 |
| 9 |
30/10/2023 |
A short history of GWs (ctd.) GWs at the
Chapel Hill conference (1957). The Newtonian limit.
Linearized gravity. |
Handouts: Newtonian limit;
Linearized gravity
Slides on the history of gravitational waves Link to P. Saulson's presentation on Pirani's contribution |
17 |
| 10 |
9/11/2023 | The Lorentz gauge. Gravitational waves
(GW) in GR. The tranverse-traceless (TT) gauge.
Gravitational wave polarization. Basics of interferometric detection of gravitational waves. Basic description of instrumental effects. Interferometric detection of gravitational waves (1): the Michelson interferometer as basic scheme. |
Handouts: Sign conventions;
The
TT gauge and the detection of gravitational waves;
GW
polarizations Paper introducing GW interferometers Marco Kraans' short movie on the working principles of a GW interferometer. |
19 |
| 11 |
13/11/2023 | Interferometric detection of gravitational waves (2): Schnupp asymmetry; laser beam modulation and sidebands; overview of the Virgo optical technology. |
Slides on the
interferometric detection of gravitational waves |
21 |
| 12 |
15/11/2023 |
Interferometric detection of gravitational waves (3): fundamentals of Fabry-Perot resonators; matrix optics | Slides on the interferometric detection of gravitational waves | 22 |
| 13 |
16/11/2023 | Interferometric detection of
gravitational waves (4): optical stability of
Fabry-Perot resonators; transfer function of the
Michelson interferometer with FP arms; power recycling.
|
Slides on the interferometric detection of gravitational waves | 24 |
| 14 |
20/11/2023 | Interferometric detection of
gravitational waves (5): transfer function of the
Michelson interferometer with FP arms (ctd.); power
recycling. Generation of gravitational waves. |
Slides on the
interferometric detection of gravitational waves Handout: Generation of gravitational waves. |
26 |
| 15 |
23/11/2023 | 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. Total power emitted by a GW source. |
Handouts: Generation of gravitational waves; GW stress-energy tensor; TT-gauge GW worksheet; Diagonal metric worksheet; GW power. | 28 |
| 16 |
27/11/2023 | History of the quadrupole formula. PSR1913+16. Generic behavior of the emission during a compact binary coalescence. |
Handouts: The
quadrupole formula; Compact binary
coalescences. Slides on PSR1913+16. |
30 |
| 17 |
29/11/2023 | The Newtonian approximation for compact
binary systems (cdt.). The physics of the black hole merger GW150914. The post-Newtonian approximation. |
Handouts: Compact
binary coalescences; 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 |
32 |
| 18 |
30/11/2023 | Tests of GR. Noise sources and sensitivity of gravitational wave detectors. Introduction to the theory of thermal noises. |
Handouts: Exotic stars.
Noise sources. Slides on tests of GR in the LVK collaboration. Comment by F. Pretorius on a test of GR with GW150914. Science summary on the latest tests of GR in the O3 observing run. |
34 |
| 19 |
4/12/2023 | Introduction to the theory of thermal noises(ctd.): 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. | Handouts: Noise sources.
Links to GravitySpy and GWitchHunters |
36 |
| 20 |
7/12/2023 | Introduction to the analysis of GW
signals. Antenna patterns. Introduction to concepts of
signal analysis. |
Handouts: Antenna
patterns; Matched filters. |
38 |
| 21 |
11/12/2023 | Introduction to the analysis of GW
signals (2). Convolution theorem. Wiener-Kintchine
theorem. The background noise of GW IFOs. Matched
filters. |
Handouts: Matched filters. | 40 |
| 22 |
14/12/2023 | Introduction to the analysis of GW
signals (3). Antenna patterns in the context of GW
signal analysis. Characteristic strain. The CBC
pipelines. Excess power (unmodeled) methods. |
Handouts: Antenna
patterns 2; Characteristic
strain; Excess power
methods. |
42 |
| 23 |
18/12/2023 | Commentary of the GW150914 methods paper.
The False Alarm Rate (FAR). The LIGO Algorithm Library
(LAL). The Schwarzschild metric. |
Handouts: The
Schwarzschild metric. Link to the GW150914 methods paper. |
44 |
| 24 |
20/12/2023 | GW sources: BBH, BNS, NSBH mergers;
continuous wave sources; generalities on neutron stars;
core-collapse supernovae (CCSN). |
Kip Thorne's paper
on "Gravitational collapse and the death of a star" Slides on GW sources |
46 |
| 25 |
21/12/2023 | GW sources (ctd.): more on CCSNs; the
stochastic GW backround. The first BNS event: GW170817. Multimessenger astronomy with gravitational waves. The near- and medium-term future of GW astrophysics. |
Handouts: Note
on the Li and
Paczinski paper. Link to the paper by Li and Paczinski. Slides on GW170817 Slides on the GWTC-3 and on the future of GW research. |
48 |
