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.
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.
*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.
*Linearized theory and 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.
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)
GIANLUCA GEMME (President)
Check on the Physics webpage for details
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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.
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.