Code
Φ-533
Level
Graduate
Category
B
Teacher
A. Porfyriadis
ECTS
5
Hours
5
Semester
Winter
Display
Yes
Offered
Yes
Teacher Webpage
Goal of the course
The course is intended for graduate students as well as for undergraduates with the proper background. The basic aim of the course is to present the general theory of relativity and gravity with applications and possible extensions of the theory.
Program
Monday 11:00-13:00, Room 1
Wednesday 11:00-13:00, Room 1
Wednesday 11:00-13:00, Room 1
Syllabus
Geometric viewpoint on flat space physics, Special Relativity
Space-time interval, Lorentz transformations, Vectors and dual vectors (one-forms), Tensors, Maxwell’s equations
Riemannian geometry
Manifolds, The metric, Parallel transport and Christoffel symbols, Geodesics, Covariant differentiation, The curvature tensor, Geodesic deviation
Gravity
The Einstein equation, The Equivalence Principle, The Newtonian limit, Gravitational redshift, Lagrangian formulation, Including matter: the energy-momentum tensor, The cosmological constant, Energy conditions
Gravitational waves
Perturbation theory, Gauge transformations, The transverse-traceless gauge, The polarization of gravitational waves, Quadrupole moment, Energy and momentum carried by waves, Detection of gravitational waves
The Schwarzschild solution
Derivation of the Schwarzschild metric, Birkhoff’s theorem, Geodesics of Schwarzschild, Experimental tests, Coordinate and curvature singularities
Black Holes
The Schwarzschild black hole, Maximally extended Kruskal solution, Killing and event horizons, Charges of spacetimes: mass, angular momentum, electric charge, The Vaidya metric, Reissner-Nordstrom black holes, Kerr black holes, Penrose process, Black hole thermodynamics
Advanced topics
Causal structure and Penrose diagrams, Elements of Quantum Field Theory in flat and curved spacetime, The Unruh effect, Hawking radiation, Bekenstein-Hawking entropy/area law
Space-time interval, Lorentz transformations, Vectors and dual vectors (one-forms), Tensors, Maxwell’s equations
Riemannian geometry
Manifolds, The metric, Parallel transport and Christoffel symbols, Geodesics, Covariant differentiation, The curvature tensor, Geodesic deviation
Gravity
The Einstein equation, The Equivalence Principle, The Newtonian limit, Gravitational redshift, Lagrangian formulation, Including matter: the energy-momentum tensor, The cosmological constant, Energy conditions
Gravitational waves
Perturbation theory, Gauge transformations, The transverse-traceless gauge, The polarization of gravitational waves, Quadrupole moment, Energy and momentum carried by waves, Detection of gravitational waves
The Schwarzschild solution
Derivation of the Schwarzschild metric, Birkhoff’s theorem, Geodesics of Schwarzschild, Experimental tests, Coordinate and curvature singularities
Black Holes
The Schwarzschild black hole, Maximally extended Kruskal solution, Killing and event horizons, Charges of spacetimes: mass, angular momentum, electric charge, The Vaidya metric, Reissner-Nordstrom black holes, Kerr black holes, Penrose process, Black hole thermodynamics
Advanced topics
Causal structure and Penrose diagrams, Elements of Quantum Field Theory in flat and curved spacetime, The Unruh effect, Hawking radiation, Bekenstein-Hawking entropy/area law
Bibliography
The main textbook of the course is:
- Carroll, Sean M., Spacetime and Geometry: An Introduction to General Relativity. Cambridge University Press, 2019.
- Schutz, Bernard, A First Course in General Relativity. 2nd Edition. Cambridge University Press, 2009
- Hartle, James B., Gravity: An Introduction to Einstein’s General Relativity. Harlow: Pearson, 2003.
- Wald, Robert M., General Relativity. University of Chicago Press, 1984
- Misner, Charles W., Thorne, K. S., & Wheeler, J. A. Gravitation. Princeton University Press, 2017
- P. A.M. Dirac, General Theory of Relativity, Princeton University Press, 1996
