Fisica | GENERAL RELATIVITY

cod. 0522600020

GENERAL RELATIVITY

	0522600020
	DIPARTIMENTO DI FISICA "E.R. CAIANIELLO"

	PHYSICS
	2013/2014

PERCORSO COMUNE

	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2010
	PRIMO SEMESTRE

TEACHING UNITS

SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
FIS/02	5	40	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS
FIS/02	1	12	LAB	SUPPLEMENTARY COMPULSORY SUBJECTS

	Objectives
	* KNOWLEDGE AND UNDERSTANDING THE AIM IS TO INTRODUCE STUDENTS TO THE FUNDAMENTALS OF GENERAL RELATIVITY AND COSMOLOGY, EMPHASIZING THE GEOMETRICAL ASPECTS AND THE APPLICATIONS. * ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING THE AIM IS TO ENABLE STUDENTS TO PROCEED INDEPENDENTLY IN THE ACQUISITION OF ADDITIONAL THEORETICAL KNOWLEDGE (BEYOND THE CONTENTS OF THE COURSE) AND BE ABLE TO SOLVE SIMPLE PROBLEMS USING ONLY THE GALILEO-EINSTEIN EQUIVALENCE PRINCIPLE, OR MORE COMPLEX PROBLEMS USING METHODS OF DIFFERENTIAL GEOMETRY (TENSOR CALCULUS). * COMMUNICATION SKILLS THE COURSE WILL FACILITATE THE STUDENT'S ABILITY TO PRESENT IN A CLEAR AND RIGOROUS WAY THE GAINED KNOWLEDGE. AT THE END OF THE COURSE THE STUDENT SHOULD BE ABLE TO THINK USING THE INTIMATE CONNECTION NATURALLY EXISTING BETWEEN GEOMETRY AND MATTER. * MAKING JUDGMENTS THE STUDENTS ARE GUIDED TO LEARN IN A CRITICAL AND RESPONSIBLE WAY EVERYTHING THAT IS EXPOSED TO THEM IN THE CLASSROOM AND TO ENRICH THEIR JUDGMENT ABILITY THROUGH THE STUDY OF THE TEACHING MATERIAL INDICATED BY THE TEACHER.

* KNOWLEDGE AND UNDERSTANDING
THE AIM IS TO INTRODUCE STUDENTS TO THE FUNDAMENTALS OF GENERAL RELATIVITY AND COSMOLOGY, EMPHASIZING THE GEOMETRICAL ASPECTS AND THE APPLICATIONS.

* ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING
THE AIM IS TO ENABLE STUDENTS TO PROCEED INDEPENDENTLY IN THE ACQUISITION OF ADDITIONAL THEORETICAL KNOWLEDGE (BEYOND THE CONTENTS OF THE COURSE) AND BE ABLE TO SOLVE SIMPLE PROBLEMS USING ONLY THE GALILEO-EINSTEIN EQUIVALENCE PRINCIPLE, OR MORE COMPLEX PROBLEMS USING METHODS OF DIFFERENTIAL GEOMETRY (TENSOR CALCULUS).

* COMMUNICATION SKILLS
THE COURSE WILL FACILITATE THE STUDENT'S ABILITY TO PRESENT IN A CLEAR AND RIGOROUS WAY THE GAINED KNOWLEDGE. AT THE END OF THE COURSE THE STUDENT SHOULD BE ABLE TO THINK USING THE INTIMATE CONNECTION NATURALLY EXISTING BETWEEN GEOMETRY AND MATTER.

* MAKING JUDGMENTS
THE STUDENTS ARE GUIDED TO LEARN IN A CRITICAL AND RESPONSIBLE WAY EVERYTHING THAT IS EXPOSED TO THEM IN THE CLASSROOM AND TO ENRICH THEIR JUDGMENT ABILITY THROUGH THE STUDY OF THE TEACHING MATERIAL INDICATED BY THE TEACHER.

	Prerequisites
	CLASSICAL MECHANICS, ELECTRODYNAMICS, SPECIAL RELATIVITY, LAGRANGIAN AND HAMILTONIAN DYNAMICS, QUANTUM MECHANICS.

	Contents
	EOTVOS AND DICKE EXPERIMENTS, GALILEO-EINSTEIN EQUIVALENCE PRINCIPLE PRINCIPLE OF GENERAL COVARIANCE GEODESIC EQUATIONS AND GEOMETRIC IDENTIFICATION OF THE GRAVITATIONAL FIELD. SOME DIFFERENTIAL GEOMETRY (DIFFERENTIAL MANIFOLDS, EXTERIOR DERIVATIVE, LIE DERIVATIVE, COVARIANT DERIVATIVE, LEVI-CIVITA COVARIANT DERIVATIVE, RIEMANN AND RICCI TENSOR FIELDS, BIANCHI IDENTITY) EINSTEIN FIELD EQUATIONS, HILBERT-PALATINI VARIATIONAL PRINCIPLE, THE GRAVITATIONAL FIELD GENERATED BY A MASSIVE BODY (SCHWARZSCHILD METRIC) PRECESSION OF THE PERIHELION OF MERCURY, DEFLECTION OF LIGHT IN A GRAVITATIONAL FIELD, SCHWARZSCHILD BLACK HOLE. MAXIMAL EXTENSION OF SCHWARZSCHILD METRIC, MAXWELL'S EQUATIONS IN A GRAVITATIONAL FIELD, GRAVITATIONAL FIELD GENERATED BY A MASSIVE CHARGED BODY (REISSER AND NORDSTROM METRIC), GRAVITATIONAL FIELD GENERATED BY A ROTATING MASSIVE BODY (KERR METRIC), REISSER-NORDSTROM AND KERR BLACK HOLES, GRAVITATIONAL WAVES.

Contents

EOTVOS AND DICKE EXPERIMENTS,
GALILEO-EINSTEIN EQUIVALENCE PRINCIPLE
PRINCIPLE OF GENERAL COVARIANCE
GEODESIC EQUATIONS AND GEOMETRIC IDENTIFICATION OF THE GRAVITATIONAL FIELD.
SOME DIFFERENTIAL GEOMETRY (DIFFERENTIAL MANIFOLDS, EXTERIOR DERIVATIVE, LIE DERIVATIVE, COVARIANT DERIVATIVE, LEVI-CIVITA COVARIANT DERIVATIVE, RIEMANN AND RICCI TENSOR FIELDS, BIANCHI IDENTITY)
EINSTEIN FIELD EQUATIONS,
HILBERT-PALATINI VARIATIONAL PRINCIPLE,
THE GRAVITATIONAL FIELD GENERATED BY A MASSIVE BODY (SCHWARZSCHILD METRIC)
PRECESSION OF THE PERIHELION OF MERCURY,
DEFLECTION OF LIGHT IN A GRAVITATIONAL FIELD,
SCHWARZSCHILD BLACK HOLE.
MAXIMAL EXTENSION OF SCHWARZSCHILD METRIC,
MAXWELL'S EQUATIONS IN A GRAVITATIONAL FIELD,
GRAVITATIONAL FIELD GENERATED BY A MASSIVE CHARGED BODY (REISSER AND NORDSTROM METRIC),
GRAVITATIONAL FIELD GENERATED BY A ROTATING MASSIVE BODY (KERR METRIC),
REISSER-NORDSTROM AND KERR BLACK HOLES,
GRAVITATIONAL WAVES.

	Teaching Methods
	THE COURSE CONSISTS OF LECTURES, ENSURING IN PARTICULAR METHODS, PROOFS AND EXERCISES.

	Verification of learning
	EXAMINATION CONSISTING OF A GENERAL INTERVIEW OR IN THE PREPARATION OF A SHORT THESIS ON A TOPIC (NOT EXPLICITLY TREATED IN CLASS) AND ITS SUBSEQUENT DISCUSSION.

	Texts
	G. VILASI, HAMILTONIAN DYNAMICS, WORLD SCIENTIFIC (2001) L.LANDAU AND E.LIFCHITZ, TEORIA DEI CAMPI, EDITORI RIUNITI (2003) I.CIUFOLINI AND J.A.WHEELER, GRAVITATION AND INERTIA, PRINCETON SERIES IN PHYSICS, (1995) S. WEINBERG, GRAVITATION AND COSMOLOGY, J. WILEY (1972) R. WALD, GENERAL RELATIVITY, CHICAGO UNIVERSITY PRESS, (1984) R. D'INVERNO, INTRODUZIONE ALLA RELATIVITÀ DI EINSTEIN (CLUEB, BOLOGNA 2001) M. GASPERINI, LEZIONI DI RELATIVITÀ GENERALE E TEORIA DELLA GRAVITAZIONE, SPRINGER 2011, APPUNTI DALLE LEZIONI

Texts

G. VILASI, HAMILTONIAN DYNAMICS, WORLD SCIENTIFIC (2001)
L.LANDAU AND E.LIFCHITZ, TEORIA DEI CAMPI, EDITORI RIUNITI (2003)
I.CIUFOLINI AND J.A.WHEELER, GRAVITATION AND INERTIA, PRINCETON SERIES IN PHYSICS, (1995)
S. WEINBERG, GRAVITATION AND COSMOLOGY, J. WILEY (1972)
R. WALD, GENERAL RELATIVITY, CHICAGO UNIVERSITY PRESS, (1984)
R. D'INVERNO, INTRODUZIONE ALLA RELATIVITÀ DI EINSTEIN (CLUEB, BOLOGNA 2001)
M. GASPERINI, LEZIONI DI RELATIVITÀ GENERALE E TEORIA DELLA GRAVITAZIONE, SPRINGER 2011,
APPUNTI DALLE LEZIONI

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