The equivalence principle. Weak gravitational field. Geodesic motion. Physical interpretation of the metric tensor. Reddening of spectral lines. Inertial forces. Tensors. Covariant derivatives. The Riemann-Christoffel tensor. Field equation in vacuum. The energy-momentum tensor. Field equations in the presence of matter. Conservation laws. The Schwarzschild solution: isotropic coordinates; planetary motion; light deflection. The Hubble expansion. The Cosmic Microwave Background radiation. The Friedmann-Robertson-Walker metric. Primordial nucleosynthesis. The distance problem in cosmology. The standard model in cosmology and inflationary scenarios.
Knowledge of the basics of tensor calculus and of classical General Relativity. Acquisition of specific competences aimed at solving some problems in General Relativity. Knowledge of problems that require a General Relativity approach (gravitational collapse, gravitational waves, theoretical cosmology) and the observations that allow to validate their theoretical discussion. Skills development targeted to the prediction of observables of interest for Astrophysics and Cosmology.
KNOWLEDGE AND UNDERSTANDING:
The course includes activities for mentoring between equals performed weekly in the second half of the semester. The experience of the past years has been quite positive. The formal verification of the learning outcomes carried out at the end of the course with an oral examination. During the exam, it is required that the student has a knowledge of the program carried out during the course, but also the ability to perform logical connections between the different parts of the course and also with elements already acquired in other courses.
APPLYING KNOWLEDGE AND UNDERSTANDING:
The course consists of a theoretical training base, necessary to acquire all the necessary mathematical instruments. In the second half of the course, it pays great attention to the experimental and/or observational aspects that validate the development of the theoretical first part. It is required that the student is capable of handling the mathematical instruments to formulate specific predictions for some observable. This close connection between mathematical tool and observations has demonstrated over the years to help the student to have a full comprehension of the course content, also regarding its more formal parts.
The course provides the use of a certain number of text books, trying to emphasize the complementarity of different approaches to the topics under study. In addition to books, for some more specific topics, the student are provided with scientific articles and/or review to get him use to a less scholastic and more research-oriented reading.
The course is normally held in English. The final exam may be held either in Italian or English. In any case, the aim is also to ensure, in addition to the specific knowledge of the program, the ability to present in a synthetic but also comprehensive way the subject matter of the examination.
The content of the course covers different aspects ranging from General Relativity to statistical mechanics, to nuclear physics and plasma physics. Students are thus forced to become familiar with different techniques easily used also in other fields of physics.