General relativity - Département de Physique de l'Ecole Normale supérieure

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General relativity

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Experimental Internship - Undergraduate program
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November 14 - 18, 2022 :
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Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

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Next student seminar :
Access to the program

Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

Faculty : Marios PETROPOULOS
Tutor : Philippe GRANDCLEMENT
ECTS credits : 6
Language of instruction : Anglais
Site web :

Description

This course aims at presenting a selection of advanced topics in gravitational classical dynamics. It starts with a reminder of the basics of general relativity and Riemannian geometry. The equations of motion are displayed, and Schwarzschild and Kerr solutions obtained. The black-hole properties of the latter are then discussed with special emphasis on their thermodynamic interpretation. Follows the general study of the energy-momentum tensor accompanied with the analysis of the conserved charges of the gravitational field. The last part of the course is devoted to Cartan’s formalism and exterior calculus, applied in particular to the investigation of homogeneous spaces. These are the building blocks for cosmological applications and primer tools for gravitational instantons, useful for the quantum theory.

PROGRAMME

1. Course 1 – From Newton to Einstein along geometry, Lie derivative, covariant derivative
2. Course 2 – Torsion, Riemann, Weyl, geodesics
3. Tutorial 1
4. Course 3 – Einstein’s field equations, Killings, non-coordinate frames, Nœther’s theorem
5. Tutorial 2
6. Course 4 – Schwarzschild solution, black-hole structure
7. Course 5 – General black-hole properties, Kerr solution, thermodynamics
8. Tutorial 3
9. Course 6 – Back to the energy-momentum tensor, conserved quantities, Komar charges
10. Tutorial 4
11. Course 7 – Exterior calculus and Cartan’s formalism
12. Course 8 – Exotic items: gravitational self-duality, Bianchi foliations, instantons
13. Tutorial 5

Quick links

Next student seminar :
Access to the program

Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr