Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT

Code	Subject	
MMM1007	Relativity and Cosmology	

Section	Semester	Hours: C+S+L	Category	Type	
Applied Mathematics	2	2+2+0	speciality	optional	

Teaching Staff in Charge	Assoc.Prof. BLAGA Cristina Olivia, Ph.D., cpblaga@math.ubbcluj.ro	
Aims	The aim of the course is the acquirement of the principles of the theory of relativity, which let us obtain a model of the large scale Universe close to the observed one. We introduce a mathematical tool, physically grounded, which let us explain some observational facts unexplained in the framework of the classical theories.	
Content	I. Special relativity. Minkowski metric. Lorentz transformation. Vectors and tensors in  Minkowski space.
II. Differential forms. Exterior product. Maxwell equations written using the differential forms.
III. Differentiable varieties. The tangent space on a differential variety. Riemannian metric on a differential variety.
VI. Differential calculus with tensors. Covariant derivative. Geodesics. Curvature and torsion. Pseudo-riemannian metric.
V. Principles of general relativity. Einstein equations. Schwarzschild solution. Geodesics of Schwarzschild space-time continuum. General relativity tests (advance of the perihelium of Mercury, deviation of the light rays in the vicinity of a massive body, redshift) in Schwarzschild space-time continuum. 
VI. Compact objects. Black holes. Gravitational radiation.
VII. Cosmology. Spaces with constant curvature. Friedman equations. Models of Universe. 	
Bibliography	BERRY M.: Principles of Cosmology and Gravitation, Cambridge University Press, 1976.
2. HOBSON M.P., EFSTATHIOU G.P., LASENBY A.N.: General Relativity: An Introduction for Physicists, Cambridge University Press, 2006.
3. HUGHSTON L.P., TOD K.P.: An Introduction to General Relativity, Cambridge University Press, 1992.
4. ISLAM J.N.: An Introduction to Mathematical Cosmology, Cambridge University Press, 2004. 
5. LIGHTMAN A.P., PRESS W.H., PRICE R.H., TEUKOLSKY S.A: Problem Book in Relativity and Gravitation, Princeton University Press, 1979. 
6. MOULD R.A.: Basic Relativity, Springer, 1994.
7. SCHUTZ B.F.: A First Course in General Relativity, Cambridge University Press, 2004. 
8. STRAUMANN N.: General Relativity and Relativistic Astrophysics, Springer, 1984.	
Assessment	The mark is a weighted mean between the mark obtained for the activity during the semester (50%) and the mark obtained at the written exam at the end of semester (50%). For the evaluation of the activity during the semester we will take into account the active participation of the students to the didactical activities (25%) and the implementation of their assignments (25%).