# Unit GENERAL RELATIVITY

Course
Physics
Study-unit Code
A003096
Location
PERUGIA
Curriculum
Fisica teorica
Teacher
Marta Orselli
Teachers
• Marta Orselli
Hours
• 42 ore - Marta Orselli
CFU
6
Course Regulation
Coorte 2023
Offered
2023/24
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
English
Contents
Solutions of Einstein's equations of general relativity and the main physical consequences. Action of the gravitational field and coupling with matter. Conservation laws and symmetries . Energy and conserved charges. Black-holes. Kerr black holes. Gravitational waves. Cosmology.
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 solutions of Einstein's equations.
Knowledge of the black hole solutions, in particular that of Kerr, rotating black holes.
Black hole thermodynamics.
Gravitational waves
The main competence ( ie the ability to apply the acquired knowledge ) will be :
Ability to describe the physical consequences of curved spaces.
Prerequisites
Course on Introduction to general relativity
Teaching methods
face to face lectures, with a tablet.
Learning verification modality
Oral exam
Extended program
Basic introduction to Einstein's equations; Spherically symmetric metric; Scharzschild metric; Statement of the theorem of Birkhoff; Geodetic time and light-like in Schwarzschild geometry; Deviation of the light rays and the time-delay; Notion of Event Horizon; Kruskal coordinates; the concepts of Black-Hole, singularities and gravitational collapse in general relativity.
Hilbert action. Formulation of the first order. Conservation laws: Symmetries and Killing vectors. ADM formulation of gravity. Hamiltonian formulation of gravity; Asymptotic symmetry and definition of conserved charges; Positivity of 'energy for a gravity system. Energy and momentum of the gravitational field.
Blacks Holes: Geometry and Properties of black holes. Classical thermodynamics of black-holes. Rindler space; elements of causal structure of space-time; Hawking radiation.
Gravitational waves: linearization of Einstein's equations. Quadrupole emission. Emission of a binary system.
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