Course topics
This
is the preliminary course program (subject to change). | Lesson |
Date |
Topics |
Slides and useful links |
Hours (total) |
| 1 |
4/10/2022 |
Introduction to the course, general
overview of gravitational-wave research. (1) |
Introductory slides |
2 |
| 2 |
6/10/2022 |
Introduction to the course, general
overview of gravitational-wave research. (2) Notation. |
Short
movie with Rainer Weiss: "The sound of gravity" Handout:SR and notation |
4 |
| 3 |
11/10/2022 |
Introduction to General Relativity (1).
Riemann manifolds and curved spaces - 1. Introduction
and generalities. |
Handouts:Riemann manifolds; Vectors and 1-forms | 6 |
| 4 |
13/10/2022 | Introduction to General Relativity (2).
Riemann manifolds and curved spaces - 2. Christoffel
symbols, covariant derivative, parallel transport,
geodesic equations. |
8 |
|
| 5 |
18/10/2022 | Introduction to General Relativity (3). Riemann manifolds and curved spaces - 3. Geodesic equations from the free-particle Lagrangian. Equivalence between the two forms of geodesic equations. The Riemann curvature tensor, the Ricci tensor, the Ricci scalar. | Handout: Equivalence of
geodesic equations |
10 |
| 6 |
20/10/2022 | Introduction to General Relativity (4).
Symmetries of the Riemann and of the Ricci tensors.
Number of independent components of the Riemann and
Ricci tensors. Key principles of GR: principle of general covariance; principle of consistency; equivalence principle; experimental tests of the weak equivalence principle. |
Slides
on the key principles of GR Handouts: Symmetries of the Riemann tensor; Number of independent components of the Riemann and Ricci tensors |
12 |
| 7 |
21/10/2022 | Introduction to General Relativity (5).
Geodesic deviation. The stress-energy tensor. The
Einstein equations. The Newtonian limit. |
Handouts:Geodesic deviation; The Newtonian limit | 14 |
| 8 |
25/10/2022 | Introduction to General Relativity (6). Linearized gravity. The Lorentz gauge. Gravitational waves in GR. Basics of interferometric detection of gravitational waves. Basic description of instrumental effects. |
Handouts: Degrees of
freedom of the solutions of Einstein's equation; Linearized gravity Link to movie describing the basic of interferometric detection of GWs Links to GravitySpy and GWitchHunters |
16 |
| 9 |
27/10/2022 |
GWs a the Chapel Hill conference (1957). The tranverse-traceless gauge. Gravitational wave polarization. | Link
to P.Saulson's presentation on Pirani's contribution.
Handouts: Chapel Hill proceedings; the TT gauge; time sequence of + polarization amplitudes; extended polarization list. |
18 |
| 10 |
11/11/2022 | Interferometric detection of
gravitational waves (1): the Michelson interferometer as
basic scheme; Schnupp asymmetry; laser beam modulation
and sidebands. |
Paper
introducing GW interferometers Slides on the interferometric detection of gravitational waves |
20 |
| 11 |
15/11/2022 | Interferometric detection of gravitational waves (2): overview of the Virgo optical technology; fundamentals of Fabry-Perot resonators; matrix optics. | Slides on the interferometric detection of gravitational waves | 22 |
| 12 |
17/11/2022 | Interferometric detection of
gravitational waves (3): 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 |
| 13 |
22/11/2022 | Generation of gravitational waves.
Gravitational waves produced by simple configurations of
moving masses. Heuristic considerations. Calculation of
the Ricci tensor of GWs. The stress-energy tensor of GWs
and the energy flux. |
Handouts:GW generation; Heuristic
considerations on GW generation; Worksheet
to compute the Ricci tensor of GWs;
Diagonal metric worksheet (from T. A. Moore); The
stress-energy tensor of GWs |
26 |
| 14 |
24/11/2022 | Total power emitted by a GW source. Power
emitted by a binary system. Generic behavior of the
emission during a compact binary coalescence. |
Handouts: Total
emitted GW power; Compact binary coalescences. The first detection paper. Commentary by E. Berti. |
28 |
| 15 |
25/11/2022 | The Newtonian approximation for compact
binary systems. The physics of the black hole merger GW150914. |
Handouts: Compact
binary coalescences; Historical
facts on the quadrupole formula. Paper on the basic physics of the black hole merger GW150914 + Cover + Chandra page on RX J0806.3+1527 |
30 |
| 16 |
29/11/2022 | Noise sources and sensitivity of
gravitational wave detectors. Introduction to the theory
of thermal noises. |
Handout: Noise sources. Links to science summaries on detector sensitivity: 1, 2, 3. Paper on thermal noises by P. Saulson Link to the LIGO Documentary Series |
32 |
| 17 |
1/12/2022 | Noise sources and sensitivity of gravitational wave detectors (2). Shot noise and radiation pressure noise. The Standard Quantum Limit. | Handout: Noise sources-2. Link to science summary on detector calibration. |
34 |
| 18 |
6/12/2022 | Noise sources and sensitivity of
gravitational wave detectors (3). Squeezing of light to
beat the SQL |
Handout: Noise sources-3. Tutorial paper on the squeezing of light. Popular physics paper on squeezing by Roman Schnabel. Commentary by Philip Ball. |
36 |
| 19 |
13/12/2022 | Introduction to the analysis of GW
signals. Antenna patterns. Description of the background noise of the GW IFOs. The False Alarm Rate (FAR). |
Handout: Antenna patterns. Interactive apps on GWs. |
38 |
| 20 |
15/12/2022 | Introduction to the analysis of GW signals (2). Matched filters. | Handout: GW data analysis. |
40 |
| 21 |
16/12/2022 | Introduction to the analysis of GW
signals (3). Antenna patterns and detection volume. The
CBC pipelines. Excess power methods. Commentary of the GW150914 methods paper. |
Handouts: Antenna
patterns-2, Excess power methods. Link to GW150914 methods paper Links to popular expositions in science summaries (1,2) Popular science paper on the statistical problems of CBC parameter estimation. |
42 |
| 22 |
20/12/2022 | Overview of GW sources. |
Slides on
gravitational wave sources |
44 |
| 23 |
21/12/2022 | Overview of GW sources (ctd.). The first BNS event: GW170817. Multimessenger astronomy with gravitational waves. Cosmological observations. |
The Li and
Paczinski (LP) paper on a kilonova model. Slides on GW170817 Handout: Notes on the LP paper. GW170817 infographics and fact sheet. |
46 |
| 24 |
22/12/2022 | The gravitational-wave transient catalog
(GWTC). The near- and medium-term future of GW
astrophysics. |
Slides on GWTC Link to science summary on GWTC-3. GWTC-3 fact sheet. Online GWTC. IGWN Observing Plans. Handout: characteristic strain. |
48 |
