General relativity
### Teaching language
Suitable for English-speaking students
### 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 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](http://catalogo.up.pt/F/-?func=find-b&local_base=FCUP&find_code=SYS&request=000224998 "A first course in general relativity (Opens in a new window)"). ISBN: 0-521-25770-0
### Complementary Bibliography
Hawking Stephen 1942-2018; [The large scale structure of space-time](http://catalogo.up.pt/F/-?func=find-b&local_base=FCUP&find_code=SYS&request=000233043 "The large scale structure of space-time (Opens in a new window)"). ISBN: 0521200164
S. Weinberg; Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity
Weinberg Steven; [Gravitation and cosmology](http://catalogo.up.pt/F/-?func=find-b&local_base=FCUP&find_code=SYS&request=000238852 "Gravitation and cosmology (Opens in a new window)"). ISBN: 0-471-92567-5
### Teaching methods and learning activities
Theory and problem solving lectures.
### Evaluation Type
Distributed evaluation with final exam
### Assessment Components
Exam: 75,00%
Written assignment: 25,00%
**Total:**: 100,00%
### Amount of time allocated to each course unit
Development of report/dissertation/thesis: 30,00 hours
Autonomous study: 90,00 hours
Frequency of lectures: 42,00 hours
**Total:**: 162,00 hours
### Eligibility for exams
Attendance of theoretical/pratical lectures.
### Calculation formula of final grade
The final mark has a 75% component from the exam and a component of 25% from a written essay also presented orally. The minimum grading for the exam is 8.
### Classification improvement
Second examination round for the exam mark (75% of the total mark).
More information at: https://sigarra.up.pt/fcup/en/ucurr_geral.ficha_uc_view?pv_ocorrencia_id=509988
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General relativity
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or HaDEA. Neither the European Union nor the granting authority can be held responsible for them. The statements made herein do not necessarily have the consent or agreement of the ASTRAIOS Consortium. These represent the opinion and findings of the author(s).
