Programa-relatividad

INTRODUCCIÓN A LA RELATIVIDAD GENERAL

Álgebra Lineal, Electromagnetismo II

Introducción. Relatividad Especial. Cálculo tensorial en el espacio de Minkowski. Fluidos ideales relativistas, tensor de energía-impulso. Gravitación y curvatura. Corrimiento al rojo gravitatorio. Variedades de Riemann y la geometría espacio-temporal. Principio de Equivalencia. Cálculo Tensorial. Transporte paralelo. Derivada covariante. El tensor de curvatura. Geodésicas. Física en espacios levemente curvos. Ecuación de Einstein. Campos gravitatorios débiles. Ondas gravitatorias. Espacios con simetría esférica, métrica de Schwarzchild. Solución en el interior de las estrellas. Trayectorias en la geometría de Schwarzchild, corrimiento del perihelio en órbitas planetarias y deflección gravitatoria de la luz. Singularidades y agujeros negros. Introducción a la Cosmología relativista, la métrica de Robertson-Walker.

Libros introductorios (nivel similar al curso):
- Bernard F. Schutz, A first course in General Relativity, 2nd edition. (Cambridge University Press, Cambridge, 2009).
- Sean Carroll, SPACETIME AND GEOMETRY. Introduction to General Relativity. (Pearson Education, San Francisco, 2004).
- James B. Hartle, GRAVITY. An introduction to Einstein's General Relativity. (Pearson Education, San Francisco, 2003).
- M. P. Hobson, G. P. Efstathiou y A. N. Lasenby, General Relativity. An Introduction for Physicist, (Cambridge UniversityPress, Cambridge, 2006).
- Ray d’Inverno, Introducing Einstein's Relativity, (Clarendon Press, Oxford, 1992).
- Ta-Pei Cheng, Relativity, Gravitation, and Cosmology. A basic Introduction, (Oxford University Press, Oxford, 2005).

Libros clásicos (más avanzados que este curso)
- Robert M. Wald, General Relativity, (The University of Chicago Press, Chicago, 1984).
- L. D. Landau and E. Lifshitz, Classical Theory of Fields, forth edition (Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1994).
- Steven Weinberg, Gravitation and Cosmology: Principles and applications of the General Theory of Relativity, (John Wiley & Sons, New York, 1972).
- Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, Gravitation, (W. H. Freeman and Company, San Francisco, 1973).
- W. Pauli, Theory of Relativity, (Dover Publications, New York, 1981).
- Hermann Weyl, Space, Time, Matter, (Dover Publications, New York, 1952).
- V. Fock, The Theory of Space, Time, and Gravitation, (Pergamon Press Inc., New York, 1959).

Libros avanzados
- S. W. Hawking & G. F. R. Ellis, The large scale structure of space-time, (Cambridge University Press, Cambridge, 1973).
- S. Chandrasekhar, The Mathematical Theory of Black Holes, (Clarendon Press, Oxford,
1992).
- John Stewart, Advanced General Relativity, (Cambridge University Press, Cambridge, 1991).
- Stephani, H., Kramer, D., Maccallum, M., Hoenselaers, C., Herlt, E.: Exact Solutions to Einstein's Field Equations, Second edition, Cambridge Univ. Press (2003).

Libros más elementales o de divulgación
- Hermann Bondi, Relativity and Common Sense, (Dover Publications, New York, 1980).
- Wolfgang Rindler, Relativity, (Oxford University Press, Oxford, 2001).
- Robert M. Wald, Space, Time, and Gravity, (The University of Chicago Press, Chicago, 1992).
- Robert Geroch, General Relativity from A to B, (The University of Chicago Press, Chicago, 1981).
- Erwin SchrÄodinger, Space-Time Structure, (Cambridge University Press, Cambridge, 1950).
- P. A. M. Dirac, General Theory of Relativity, (Princeton University Press, Princeton, 1996).
- G. 't Hooft, Introduction to General Relativity, Caputcollege 1998, Utrecht University.

Geometría Diferencial
- Bernard F. Schutz, Geometrical methods of mathematical physics, (Cambridge University Press, Cambridge, 1980).
- Barret O0Neill, Elementary Differential Geometry, (Academic Press Inc., New York, 1966).
- Barret O0Neill, Semi-Riemanian Geometry, (Academic Press, San Diego, 1983).
- Harley Flanders, Differential Forms, (Academic Press, New York, 1963).
- L. P. Eisenhart, Riemannian Geometry, (Princeton University Press, 1949).