General Relativity

Code	17557
Year	1
Semester	S1
ECTS Credits	6
Workload	TP(60H)
Scientific area	Physics
Entry requirements	None.
Learning outcomes	In this course unit, students will learn the fundamentals of General Relativity, from the formulation of the equivalence principle to an introduction to the most modern techniques in numerical relativity. Students should acquire knowledge and skills on: aspects of the mathematical formulation of general relativity, the solutions of Einstein's field equations, the linearization of field equations. Topics on numerical relativity will also be explored, to be selected according to the students' interests.
Syllabus	1- Equivalence principle a. Gravitational mass and inertial mass b. Gravitation and geometry 2- Differential geometry a. Manifolds b. Affine Spaces c. Riemannian manifolds 3- Gravitation a. Motion in Curved Spacetime b. The gravitational field and Einstein field equations c. Linearized gravitation 4- Black holes a. The. Schwarzschild's solution b. Charged black holes and Reissner-Nordström solution c. Rotating Black holes and Kerr-Newman solution 5- Basic notions of numerical relativity
Main Bibliography	- Robert M. Wald (1984) General Relativity. Chicago Univ. Pr. doi:10.7208/chicago/9780226870373.001.0001 - Griffiths, D., Derbes, D., & Sohn, R. (Eds.). (2022). Sidney Coleman's Lectures on Relativity. Cambridge: Cambridge University Press. doi:10.1017/9781009053716 - Baumgarte, T., & Shapiro, S. (2021). Numerical Relativity: Starting from Scratch. Cambridge: Cambridge University Press. doi:10.1017/9781108933445
Teaching Methodologies and Assessment Criteria	An interactive, “hands-on” approach like the one proposed above is the best suited for learning the topics that form the syllabus of this CU, and to fulfill its learning outcomes. In addition to a written test (60%), assessment includes work by students, with presentation and open discussion (40%)
Language	Portuguese. Tutorial support is available in English.