Unit INTRODUCTION TO GENERAL RELATIVITY
- Course
- Physics
- Study-unit Code
- GP005462
- Location
- PERUGIA
- Curriculum
- In all curricula
- Teacher
- Marta Orselli
- Teachers
-
- Marta Orselli
- Hours
- 42 ore - Marta Orselli
- CFU
- 6
- Course Regulation
- Coorte 2020
- Offered
- 2022/23
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- FIS/02
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- italian
- Contents
- Equivalence principle. Einstein's equations. Schwarzschild solution. Black Holes. Schwarzschild black hole solution. Reissner Nordstrom black hole solution.
- Reference texts
- S. M. Carroll, Spacetime and Geometry, Addison Wesely (2004).
S. Weinberg, Gravitation and Cosmology, Wiley (1972). - Educational objectives
- The main aim of this teaching is to provide students with the bases needed to address and solve the most important problems in General Relativity.
Main knowledge acquired will be:
Knowledge of the principles of general relativity.
Knowledge of Einstein's equations .
Knowledge of certain black hole solutions.
The main competence ( ie the ability to apply the acquired knowledge ) will be :
Ability to describe the physical consequences of curved spaces.
Knowing how to discuss symmetries and physical properties of solution of Einstein's equations. - Prerequisites
- basic knowledge on special relativity.
- Teaching methods
- face to face
- Other information
- Learning verification modality
- Oral exam
- Extended program
- Basic introduction to special relativity. Equivalence principle. Gravitational red-shift and gravitational time-dilation. The metric. Geodesic equation and it's classical limit. Tensors. Covariant derivative. Covariant formulation of the geodesic equation. Covariant definition of acceleration. Parallel transport. Definition of curvature. Riemann tensor and its properties. Einstein's equations; Einstei-Hilbert action. Vacuum energy and Cosmological constant. Spherically symmetric metric; Scharzschild metric. Birkhoff theorem; Geodetic time-like and light-like in Schwarzschild geometry; Deviation of the light rays and the time-delay;
Hamiltonian formulation of gravity; Asymptotic symmetry and definition of conserved charges;
Blacks Holes: Geometry and Properties of black holes. Definitio of asymptotically flat spacetime, stationary spacetime and static spacetime. Killing vector fields for the Scwarzschild metric. Causal structure of spacetime. Notion of Event Horizon; Kruskal coordinates; the concepts of Black-Hole, singularities and gravitational collapse in general relativity. Reissner Nordstrom black hole solution. Wormhole solution.