The aim of this course is that of introducing the basic notions of the modern theory of gravitation, general relativity, an its main conceptual and astrophysical implications.
Main Topics:
- Newtonian theory and its shortcomings. The equivalence principle and its role in Einstein's formulation of gravity. - Geodesic equations as a consequence of the equivalence principle.
- Differentiable manifolds, vectors, one-forms, tensors. The metric tensor.
- Parallel transport an covariant derivative. The curvature tensor.
- Energy-momentum tensor. General covariance.
- Einstein equations for the gravitational field.
- The Einstein-Hilbert action and the Lagrangian formulation of General Relativity.
- Symmetries, Killing vectors and conservation laws.
- Static, spherically symmetric solution of Einstein’s equations: the Schwarzschild spacetime. Concept of black hole and of event horizon.
- Singularities in General Relativity. Geodesics of Schwarzschild’s spacetime.
- Kinematical tests of General Relativity: gravitational redshift, light deflection, periastron precession, Shapiro time delay. The black hole shadow.
- Gravitational waves as perturbations of flat spacetime. Geodesic deviation of gravitational waves. The effects of a gravitational waves on matter, basic principles of gravitational-wave interferometers.
- Gravitational waves in the quadrupolar approximation. Energy carried by a gravitational wave. Gravitational wave emission by compact binaries.
Main Topics:
- Newtonian theory and its shortcomings. The equivalence principle and its role in Einstein's formulation of gravity. - Geodesic equations as a consequence of the equivalence principle.
- Differentiable manifolds, vectors, one-forms, tensors. The metric tensor.
- Parallel transport an covariant derivative. The curvature tensor.
- Energy-momentum tensor. General covariance.
- Einstein equations for the gravitational field.
- The Einstein-Hilbert action and the Lagrangian formulation of General Relativity.
- Symmetries, Killing vectors and conservation laws.
- Static, spherically symmetric solution of Einstein’s equations: the Schwarzschild spacetime. Concept of black hole and of event horizon.
- Singularities in General Relativity. Geodesics of Schwarzschild’s spacetime.
- Kinematical tests of General Relativity: gravitational redshift, light deflection, periastron precession, Shapiro time delay. The black hole shadow.
- Gravitational waves as perturbations of flat spacetime. Geodesic deviation of gravitational waves. The effects of a gravitational waves on matter, basic principles of gravitational-wave interferometers.
- Gravitational waves in the quadrupolar approximation. Energy carried by a gravitational wave. Gravitational wave emission by compact binaries.
- Teacher: STEFANO BOLOGNESI
- Teacher: LEONARDO GUALTIERI