Make the student familiar with the theoretical underpinnings of General Relativity, both as a geometric theory of space-time and by stressing analogies and differences with the field theories based on local symmetries that describe the interactions among elementary particles. Illustrate the basic elements of differential geometry needed to correctly frame the various concepts. Introduce the student to extensions of the theory of interest for current research.
Curriculum
teacher profile teaching materials
General covariance. Local inertial systems. References to Special Relativity. Noether's theorem. Curvilinear coordinates.
Christoffel symbols. Geodesic. Covariant derivation. Curvature. Geodesic deviation. Well tensor.
Einstein-Hilbert action. Identity of Palatine. Analogies with spin gauge theories 1. Couplings: tensor
pulse-energy, scalar field and electromagnetic field. Linear approximation and Fierz-Pauli theory. Gravitational waves.
Gravity as a self-interacting theory for a zero-mass field of spin 2. Noether's method. Isometries and Killing equation.
Lie derivative. Maximally symmetrical spaces. Formulation of Cartan-Weyl and fermionic couplings. The solution of
Schwarzschild. Black holes. Gravitational field energy. Asymptotically flat spaces.
(Addison-Wesley 2014/Cambridge University Press, 2019)
- Hawking S W and Ellis G F R, ``The Large Scale Structure of Space-Time'' (Cambridge
University Press, 1973).
- Freedman D Z and Van Proyen A, ``Supergravity'' (Cambridge University Press,
2012).
- Ortin T, ``Gravity and Strings'' (Cambridge University Press, 2004)
- Wald R, ``General Relativity'' (The University of Chicago Press, 1984).
- Weinberg S, ``Gravitation and Cosmology - principles and applications of the gen-
eral theory of relativity'' , (John Wiley & Sons, 1972).
Fruizione: 20402258 TEORIA DELLA RELATIVITA' in Fisica LM-17 FRANCIA DARIO
Programme
Inertia and invariance in Galilean Relativity and Special Relativity. The principle of equivalence.General covariance. Local inertial systems. References to Special Relativity. Noether's theorem. Curvilinear coordinates.
Christoffel symbols. Geodesic. Covariant derivation. Curvature. Geodesic deviation. Well tensor.
Einstein-Hilbert action. Identity of Palatine. Analogies with spin gauge theories 1. Couplings: tensor
pulse-energy, scalar field and electromagnetic field. Linear approximation and Fierz-Pauli theory. Gravitational waves.
Gravity as a self-interacting theory for a zero-mass field of spin 2. Noether's method. Isometries and Killing equation.
Lie derivative. Maximally symmetrical spaces. Formulation of Cartan-Weyl and fermionic couplings. The solution of
Schwarzschild. Black holes. Gravitational field energy. Asymptotically flat spaces.
Core Documentation
- Carroll S, ``Spacetime and Geometry: An Introduction to General Relativity’'(Addison-Wesley 2014/Cambridge University Press, 2019)
- Hawking S W and Ellis G F R, ``The Large Scale Structure of Space-Time'' (Cambridge
University Press, 1973).
- Freedman D Z and Van Proyen A, ``Supergravity'' (Cambridge University Press,
2012).
- Ortin T, ``Gravity and Strings'' (Cambridge University Press, 2004)
- Wald R, ``General Relativity'' (The University of Chicago Press, 1984).
- Weinberg S, ``Gravitation and Cosmology - principles and applications of the gen-
eral theory of relativity'' , (John Wiley & Sons, 1972).
Type of delivery of the course
the lessons take place in the classroom in frontal modeType of evaluation
the exam consists only of an oral exam teacher profile teaching materials
General covariance. Local inertial systems. References to Special Relativity. Noether's theorem. Curvilinear coordinates.
Christoffel symbols. Geodesic. Covariant derivation. Curvature. Geodesic deviation. Well tensor.
Einstein-Hilbert action. Identity of Palatine. Analogies with spin gauge theories 1. Couplings: tensor
pulse-energy, scalar field and electromagnetic field. Linear approximation and Fierz-Pauli theory. Gravitational waves.
Gravity as a self-interacting theory for a zero-mass field of spin 2. Noether's method. Isometries and Killing equation.
Lie derivative. Maximally symmetrical spaces. Formulation of Cartan-Weyl and fermionic couplings. The solution of
Schwarzschild. Black holes. Gravitational field energy. Asymptotically flat spaces.
(Addison-Wesley 2014/Cambridge University Press, 2019)
- Hawking S W and Ellis G F R, ``The Large Scale Structure of Space-Time'' (Cambridge
University Press, 1973).
- Freedman D Z and Van Proyen A, ``Supergravity'' (Cambridge University Press,
2012).
- Ortin T, ``Gravity and Strings'' (Cambridge University Press, 2004)
- Wald R, ``General Relativity'' (The University of Chicago Press, 1984).
- Weinberg S, ``Gravitation and Cosmology - principles and applications of the gen-
eral theory of relativity'' , (John Wiley & Sons, 1972).
Fruizione: 20402258 TEORIA DELLA RELATIVITA' in Fisica LM-17 FRANCIA DARIO
Programme
Inertia and invariance in Galilean Relativity and Special Relativity. The principle of equivalence.General covariance. Local inertial systems. References to Special Relativity. Noether's theorem. Curvilinear coordinates.
Christoffel symbols. Geodesic. Covariant derivation. Curvature. Geodesic deviation. Well tensor.
Einstein-Hilbert action. Identity of Palatine. Analogies with spin gauge theories 1. Couplings: tensor
pulse-energy, scalar field and electromagnetic field. Linear approximation and Fierz-Pauli theory. Gravitational waves.
Gravity as a self-interacting theory for a zero-mass field of spin 2. Noether's method. Isometries and Killing equation.
Lie derivative. Maximally symmetrical spaces. Formulation of Cartan-Weyl and fermionic couplings. The solution of
Schwarzschild. Black holes. Gravitational field energy. Asymptotically flat spaces.
Core Documentation
- Carroll S, ``Spacetime and Geometry: An Introduction to General Relativity’'(Addison-Wesley 2014/Cambridge University Press, 2019)
- Hawking S W and Ellis G F R, ``The Large Scale Structure of Space-Time'' (Cambridge
University Press, 1973).
- Freedman D Z and Van Proyen A, ``Supergravity'' (Cambridge University Press,
2012).
- Ortin T, ``Gravity and Strings'' (Cambridge University Press, 2004)
- Wald R, ``General Relativity'' (The University of Chicago Press, 1984).
- Weinberg S, ``Gravitation and Cosmology - principles and applications of the gen-
eral theory of relativity'' , (John Wiley & Sons, 1972).
Type of delivery of the course
the lessons take place in the classroom in frontal modeType of evaluation
the exam consists only of an oral exam