Università Roma Tre

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.

- 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).