General Relativity

Code:

F4031

Acronym:

F4031

Keywords
Classification	Keyword
OFICIAL	Physics

Instance: 2024/2025 - 1S

Active?	Yes
Responsible unit:	Department of Physics and Astronomy
Course/CS Responsible:	Master in Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:A_ASTR	7	Study plan since academic year 2024/2025	1	-	6	42	162
			2
M:F	17	Official Study Plan	1	-	6	42	162
M:M	9	Official study plan since 2024/2025	1	-	6	42	162
			2

Teaching language

Portuguese and english

Objectives

The aim is to introduce the main ideas about the general theory of relativity, according to which the space-time curvature and dynamics are determined by its energy-matter content. For reach this level of understanding, the physical and mathematical principles of this formulation will be discussed.

To develop skils in theoretical physics.

Learning outcomes and competences

Adquire the geometrical concepts associated to Einstein gravity, as well as to understand the importance of this theory to describe physical phenomena.

Working method

À distância

Program

1. Special Relativity - Lorentz group and transformations - Vectors e Tensors - Electrodynamics 2. Einstein's Equivalence Principle - Clock Postulate and the Universality of the gravitational redshift and the geodesic deviation - Weak Equivalence Principle - Covariance under local Lorentz transformations - Covariance under position transformations - Schiff's conjecture - Princípio de Equivalência Forte 3. Generalized Covariance Principle 4. Introduction to Differential Geometry - Manifolds - Exterior derivative and Lie derivative - Covariant derivative - Curvature tensor - Metric 5. Einstein's General Relativity - Energy-Momentum tensor - Einstein's field equations - Newtonian limit, linear approximation of Einstein's field equations and gravitational waves - Matter fields - Lagrange formulation (Einstein-Hilbert action, bosonic string action and corrections to the Einstein-Hilbert action) - Classic tests: Deflection of light and radar eco delay in the vicinity of the sun, and advance precession of Mercury's perihelion 6. Exact Solutions of Einstein's field equations - Minkowski, De Sitter e anti-De Sitter space-time - Schwarzschild's black hole solution - Robertson-Walker space-time Bibliography: - S. Weinberg, ``Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity'' (John Wiley and Sons, New York 1972). Chapters: 1, 2, 3, 4, 7, 8. - S.W. Hawking and G.F.R. Ellis, ``The Large Scale Structure of Space-Time'' (Cambridge University Press, Cambridge 1973). Chapters: 1, 2, 3. - C.W. Misner, K.S. Thorne and J.A. Wheeler, ``Gravitation'' (Freeman, San Francisco, 1974). - ``300 Years of Gravitation'', Eds. S.W. Hawking and W. Israel (Cambridge University Press, Cambridge 1987). Capítulos: 4 e 5. - R.M. Wald, ``General Relativity'', (The University of Chicago Press, Chicago 1984). Chapters: 1, 2, 3, 4, 5, 6. - C.M. Will, ``Theory and experiment in gravitational physics'' (Cambridge University Press, Cambridge 1993). Capítulos: 1, 2, 3 e 14. - G.G. Ross, ``Grand Unified Theories'' (Benjamin/Cummings, Menlo Park, California 1984). Chapters: 2, 3, 4 and 12. - M.B. Green, J.H. Schwarz and E. Witten, ``Superstring Theory Vol. 1 Introduction'' (Cambridge University Press, 1987). Chapters: 2. - E.W. Kolb e M.S. Turner, ``The Early Universe'' (Addison-Wesley P. C., 1990). Chapters: 1, 3, 4, 5 and 8. - P.J.E. Peebles, D.N. Schramm, E.L. Turner e R.G. Kron, Nature, 352 (1991) 769. - O. Bertolami, ``Modelo Cosmológico Padrão: uma breve introdução'', "Agregação" lecture, Instituto Superior Técnico, July 1996.

Mandatory literature

Schutz Bernard F.; A first course in general relativity. ISBN: 0-521-25770-0

Complementary Bibliography

Hawking Stephen 1942-2018; The large scale structure of space-time. ISBN: 0521200164
S. Weinberg; Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity
Weinberg Steven; Gravitation and cosmology. ISBN: 0-471-92567-5

Teaching methods and learning activities

Theory and problem solving lectures.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	80,00
Trabalho escrito	20,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Elaboração de relatório/dissertação/tese	30,00
Estudo autónomo	90,00
Frequência das aulas	42,00
Total:	162,00

Eligibility for exams

Attendance of 70% of the theoretical/exercise lectures.

Calculation formula of final grade

The final mark has a 80% component from the exam and a component of 20% from a written essay also presented orally. The minimum grading for the exam is 8. 

Classification improvement

Second examination round for the exam mark (80% of the total mark).

Observations

Evaluation panel:

 

Orfeu Bertolami, Miguel Costa, Caroline Silva