General relativity

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Stages L3
Stages M1 ICFP

Actualités : Séminaire de Recherche ICFP
du 15 au 19 novembre 2021 :

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Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

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Faculty : Daniele Steer
Tutor : Filippo Vernizzi
ECTS credits : 6
Language of instruction  : English
Examination :
Site web :

Description

The aim of this course is to present a selection of advanced topics in classical gravitational dynamics. After reminder of the basics of General Relativity (GR)and Riemannian geometry, we initially focus on black-holes. We discuss different such solutions (Schwarzschild, Kerr) and their properties : we introduce Penrose diagrams ; event horizons and Killing horizons ; conserved charges and currents ; black-hole thermodynamics and Hawking radiation. Elements of black-hole perturbation theory are also discussed : indeed perturbed black-holes can be sources of gravitational waves (GWs), which can be searched for with current and future detectors such as LIGO-Virgo and LISA. In this context, gravitational waves and their sources — including perturbed black-holes but also binaries of different compact objects (black holes and/or neutron stars) — form another important part of this course. There we discuss the linearised Einstein equations (including the quadrupole formula and the energy in GWs). We determine the GW signal from black-hole binaries (to first order in the post-Newtonian expansion), and discuss the latest results from the LIGO-Virgo GW detectors. This includes properties of the populations of black-holes observed, as well as tests of GR. A third part of the course will focus on cosmological solutions of Einsteins equations. There we will also discuss how certain cosmological parameters, such as the Hubble constant (whose value is currently a source of tension), can be measured with GW observations. The stochastic gravitational wave background will also be introduced. The last part of the course touches on advanced topics : this may include theories of gravity beyond GR (and how they can be tested with GWs) ; and a quantum field theoretic description of general relativity, namely a modern approach to gravity in which the gravitational force is carried by spin-2 gravitons.

Prerequisites : a first basic course in GR is assumed.

Books :

• Lecture Notes on General Relativity, M.Blau,
http://www.blau.itp.unibe.ch/GRLecturenotes.html

• Spacetime and geometry, S.Carroll, (2014, Pearson publishers).

• General Relativity, R.Wald, (1984, The University of Chicago Press)

• Gravitation and Cosmology : Principles and applications of the general theory of relativity, S.Weinberg (1972, Wiley)

• Cosmology, S.Weinberg, (2008, Oxford University Press)

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

• Gravitational Waves : Volume 2 : Astrophysics and cosmology, M.Maggiore, (Oxford University Press, 2018).

• Gravity. Newtonian, post-newtonian, relativistic, E.Poisson and C.M.Will, (Cambridge University Press, 2014.)

Accès rapides

Prochain Séminaire de la FIP :
Accéder au programme

Retrouvez toutes les informations pour vos stages :
Stages L3
Stages M1 ICFP

Actualités : Séminaire de Recherche ICFP
du 15 au 19 novembre 2021 :

Retrouvez le programme complet

Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

r>