# 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
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.
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