. "General relativity"@en . . "6.0" . "### Teaching language\n\nSuitable for English-speaking students\n\n### Objectives\n\nThe 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. \n \nTo develop skils in theoretical physics.\n\n### Learning outcomes and competences\n\nAdquire the geometrical concepts associated to Einstein gravity, as well as the importance of this theory to describe physical phenomena.\n\n### Working method\n\nÀ distância\n\n### Program\n\n1\\. 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.\n\n### Mandatory literature\n\nSchutz 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 \n\n### Complementary Bibliography\n\nHawking 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 \nS. Weinberg; Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity \nWeinberg 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 \n\n### Teaching methods and learning activities\n\nTheory and problem solving lectures.\n\n### Evaluation Type\n\nDistributed evaluation with final exam\n\n### Assessment Components\n\nExam: 75,00%\nWritten assignment: 25,00%\n\n**Total:**: 100,00%\n\n### Amount of time allocated to each course unit\n\nDevelopment of report/dissertation/thesis: 30,00 hours\nAutonomous study: 90,00 hours\nFrequency of lectures: 42,00 hours\n\n**Total:**: 162,00 hours\n\n### Eligibility for exams\n\nAttendance of theoretical/pratical lectures.\n\n### Calculation formula of final grade\n\nThe 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.\n\n### Classification improvement\n\nSecond examination round for the exam mark (75% of the total mark).\n\nMore information at: https://sigarra.up.pt/fcup/en/ucurr_geral.ficha_uc_view?pv_ocorrencia_id=509988" . . "Presential"@en . "TRUE" . . "Classical Mechanics"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Master in Astronomy and Astrophysics"@en . . "https://sigarra.up.pt/fcup/en/cur_geral.cur_view?pv_ano_lectivo=2022&pv_origem=cur&pv_tipo_cur_sigla=m&pv_curso_id=871" . "120"^^ . "Presential"@en . "The main objective of the Master of Astronomy is to complement and extend the training of graduate students in astronomy, physics, mathematics and related fields. In particular, in order to improve their preparation for a research career in Astronomy, through their subsequent enrolment in a Doctoral Programme in Astronomy.\n\n### Admissions Requirements\n\nApplicants to the Second Cycle (Master) in Astronomy must hold a First Cycle (Bachelor) degree (minimum of 180 ECTS credits) or equivalent (including higher education foreign degrees), whose curriculum includes at least 30 ECTS credits, or equivalent, in Mathematics and Physics, including a minimum of 12 ECTS credits in each of these scientific areas. Candidates that may verify these conditions before the end of the registration period in the Master in Astronomy can also apply. Holders of an academic, scientific or professional curriculum that is recognised as attesting the capacity to successfully complete this cycle of studies by the Scientific Committee of the Master in Astronomy may also be admitted. \n\n### Criteria for Selection and Ranking\n\nThe ranking will be done according to the following criteria and sub-criteria:\n\n* 1.1 - Academic curriculum (training area and average grade) (80%)\n * 1.1.1 - Subcriterion 1: training area (40%)\n * 1.1.2 - Subcriterion 2: average and adequacy of the degree (40%)\n* 1.2 - Scientific curriculum and professional experience (20%)\n * 1.2.1 - Subcriterion 1: technical and/or scientific publications and communications (10%)\n * 1.2.2 - Subcriterion 2: participation in research projects, internships in the area of the cycle of studies or other relevant professional experience (10%)\n\n \nNote: Candidates who do not yet hold a Bachelor's degree and/or have an academic, scientific or professional curriculum which is recognized as attesting the capacity to carry out this cycle of studies by the statutory competent scientific body, will be ranked according to the criteria and subcriteria indicated above, with the difference that the final average mark of the degree will be replaced by the weighted average mark of all curricular units completed to date. \n \n**Candidates' tiebreaker criterion:** greater number of ECTS credits obtained in the area of the cycle of studies.\n\n### Teaching Language\n\n* Fully in English\n\n### Information\n\nIt is highly desirable that candidates possess programming skills and a good written and oral command of the English language.\n\n### Contacts\n\nCourse Director: m.ast.diretor@fc.up.pt\n\nPostgraduate Section: pos.graduacao@fc.up.pt\n\nStudents: m.ast@fc.up.pt\n\n### General information\n\n* Information for applicants: https://sigarra.up.pt/fcup/en/cur_geral.cur_info_cand_view?pv_curso_id=871&pv_ano_lectivo=2022&pv_tipo_cur_sigla=m&pv_origem=cur \n\nDirector: Catarina Lobo\n\nAcronym: M:A_ASTR\n\nAcademic Degree: Master\n\nType of course/cycle of study: Masters Degree\n\nStart: 2007/2008\n\nDuration: 4 Semesters\n\n### Study Plan\n\n* Plano de Estudos oficial desde 2013/14: https://sigarra.up.pt/fcup/en/cur_geral.cur_planos_estudos_view?pv_plano_id=6001&pv_ano_lectivo=2022&pv_tipo_cur_sigla=m&pv_origem=cur \n\n* All Courses of Study: https://sigarra.up.pt/fcup/en/cur_geral.cur_planos_estudos_list?pv_curso_id=871&pv_ano_lectivo=2022&pv_tipo_cur_sigla=m&pv_origem=cur \n\n### Certificates\n\n* Master's degree in Astronomy and Astrophysics (120 ECTS credits)\n* Specialization in Astronomy and Astrophysics (66 ECTS credits)\n\n### Predominant Scientific Areas\n\n* Astronomy\n* Physics"@en . . . . "2"@en . "FALSE" . . . "Master"@en . "Thesis" . "1300.00" . "Euro"@en . "3750.00 (International) / 2250.00 (CPLP)" . "Recommended" . "* Researcher: Researchers in astronomy work on a variety of projects, from studying the formation of stars and galaxies to searching for exoplanets. They typically work in universities, research institutes, or government agencies.\n* Engineer: Engineers in astronomy develop and build instruments for astronomical observations. They also work on software for data analysis and visualization.\n* Consultant: Consultants in astronomy work with businesses and government agencies to apply astronomical knowledge to solve problems. For example, they may help to develop new technologies for space exploration or to assess the risks of asteroid impacts.\n* Science communicator: Science communicators in astronomy share the excitement of astronomy with the public through writing, public speaking, and media appearances. They may work in museums, science centers, or the media."@en . "1"^^ . "TRUE" . "Upstream"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .