1) M. Nakahara, "Geometry, Topology and Physics"
2) S. Carroll, "Spacetime and Geometry: An Introduction to General Relativity"
3) R. Wald, "General Relativity"
4) P. Townsend, "Black Holes"
5) Dispense Prof. D. Seminara
Learning Objectives
Knowledge acquired: Mathematical skills for GR. Foundations of GR
Competence acquired: Derivation of Einsten Equations. Notable examples of GR solutions
Skills acquired (at the end of the course): Computing geometrical quantities for pseudo-Riemannian manifold. Computing Einstein equations for a given ansatz of the metric
Prerequisites
No mandatory prerequisites. For a better comprehension of the course's content, the student should be familiar with the basic principles of special relativity and cinematics, as well as the standard formulation of electromagnetism.
Teaching Methods
6 CFU
Lectures hours: 48
Further information
Office hours appointment by email: cotrone@fi.infn.it
Type of Assessment
Oral test, about one hour long. The student will be asked to discuss 3-4 topics. Assessment: the student is required to use the appropriate language to show the comprehension of the basic physical processes, and how the outcomes depend on the assumptions. In order to determine the student's comprehension of the subject, further questions will be posed during the exposition. The student is required to be able to perform order-of-magnitude estimates of basic observableas, as well as detailed calculations employing the appropriate mathematical framework when necessary.
Course program
Mathematical Structures needed to describe a curved space: manifolds and (pseudo-)Riemannian geometry.
Einstein equations, Hilbert-Einstein action.
Horizons, singularities, causal structure, black holes. Charged and rotating black holes. Conserved quantities.