OVERVIEW

The course starts from the exposition of introductory elements of the theory of general relativity, providing the necessary tools for the understanding of the properties of gravitational waves, arriving at the study of modern experimental techniques used in gravitational wave detectors. The recent discovery of gravitational waves and its consequences for fundamental physics and astrophysics are discussed in the last part of the course.

AIMS AND CONTENT

LEARNING OUTCOMES

The course gives an updated overview on the activity of experimental research in the theory of gravitation based on its fundamentals (test of the weak equivalence principle: Eötvös experiment, experiment Roll, Dicke and Krotkov; experiment Braginsky and Panov) up to recent interferometric detectors of gravitational waves (Fabry-Perot interferometers with the cavity, the optical design of Virgo, noise sources and mitigation strategies). Part of the course is dedicated to gravitational astrophysics elements (compact astrophysical objects, rotating neutron stars, stellar collapse), with particular reference to general relativity tests.

AIMS AND LEARNING OUTCOMES

The course aims to provide students with the tools necessary for the understanding of modern scientific literature in the field of gravitational waves, gravitational astronomy and multi-messenger astronomy, as well as a good knowledge of modern experimental techniques and data analysis used for signal detection gravitational.

TEACHING METHODS

Frontal lessons

SYLLABUS/CONTENT

Elements of general relativity
Equivalence principle. Algebra of tensors. Tensor equations. Geodetic curves. Covariant derivative. Geodesic deviation and curvature. Riemann tensor. Energy-impulse tensor. Einstein's equation. Weak-field limit.

Gravitational waves
Gravitational waves as solutions to Einstein's equations. Expression in TT (Transverse-Traceless) gauge and in the laboratory system. Effect on test masses. Gravitational wave generation. Intensity and brightness of the sources of gravitational waves.

Elements of gravitational astrophysics
Compact astrophysical objects. Rotating neutron stars. Star collapse. Cosmological background of gravitational waves. Coalescence of binary systems. PSR B1913 + 16. Double pulsar PSR J0737-3039. General relativity test with GW150914 and GW151226.

Interferometric detectors of gravitational waves
A simple Michelson interferometer. Interferometers with Fabry-Pérot cavities. Power recycling. Virgo's optical scheme. Noise sources and mitigation strategies (quantum noise, fluctuation-dissipation theorem and thermal noise, seismic noise, Newtonian noise).

Elements of analysis of stochastic processes
Stochastic processes. Media, variance, correlation, autocorrelation. Harmonic process. Poisson process. Systems without memory. Hypothesis test. Permutation test. Linear transformations. Power spectrum. Matched filtering. False alarm rate, sampling in the parameter space.

Advanced detection techniques
Controls and locking: Pound-Drever-Hall technique. Signal recycling. Techniques for overcoming the quantum limit: squeezing. Third generation interferometric detectors. Detectors in space. Pulsar timing array.

RECOMMENDED READING/BIBLIOGRAPHY

T.A. Moore, A General Relativity Workbook, University Science Books (2013)

M. Maggiore, Gravitational Waves. Volume 1: Theory and Experiments, Oxford University Press (2008)

P.R. Saulson, Fundamentals of Interferometric Gravitational Wave Detectors, World Scientific (1994)

M. Bassan (Ed.), Advanced Interferometers and the Search for Gravitational Waves, Springer (2014)

J. D. E. Creighton, W. G. Anderson, Gravitational-Wave Physics and Astronomy: An Introduction to Theory, Experiment and Data Analysis, Wiley (2011)

TEACHERS AND EXAM BOARD

Exam Board

GIANLUCA GEMME (President)

ANDREA CHINCARINI

FIODOR SORRENTINO

SILVANO TOSI

LESSONS

LESSONS START

March 7, 2018

Class schedule

GRAVITATIONAL WAVES

EXAMS

EXAM DESCRIPTION

Presentation of a written essay on one of the topics covered in the course.
Discussion of the essay and discussion on the topics covered in the course.

ASSESSMENT METHODS

The student is required to present a short paper in English on a topic agreed upon with the teacher, typically an in-depth study of a topic covered during the course.

The discussion of the dissertation is carried out before the examination committee composed of the responsible teacher and another expert of the subject and consists of a presentation lasting 20-30 minutes. During the presentation, and following it, the committee addresses to the student questions concerning the examination program and which allow the commission to evaluate, in addition to the preparation, the degree of clarity, and the ability to autonomously elaborate the contents. of the course achieved by the student.

The final evaluation is obtained from a weighted average of the evaluations of the clarity and completeness of the written work, of the clarity and completeness of the exposition and of the autonomous elaboration capacity of the student.