OVERVIEW

These lectures will give an extended presentation of General Relativity, that is the relativistic theory of gravitation published by Einstein in 1916. Besides the classical applications ot physics (cosmology, gravitational lensing, black-hole), one will stress the mathematical framework required to formulate the theory in a rigourous way (that is, pseudo-Riemannian differential geometry), as well as some further mathematical developments inspired by theory. 

AIMS AND CONTENT

LEARNING OUTCOMES

The aim of the course is to provide the fundamental elements of differential geometry required for the rigorous formulation of general relativity, in particular the concepts of connection and curvature in pseudo-Riemannian spaces, and to develop the techniques needed to study Einstein’s equations.

AIMS AND LEARNING OUTCOMES

The course will provide the student with all the mathematical tools necessary to formulate the conceptual basis of general relativity.

More generally, the aim is to show how mathematics and physics harmoniously speak to each other:

- on the one side, we will see why, and how, differential geometry is the right tool to give a rigourous formulation of Einstein's intuition 

- on the other side, we will see how the final formulation of the theory (Einstein equation of general relativity) yields new mathematical developments (like singularity). 

PREREQUISITES

Previous knowledge of differential geometry and special relativity will help, but these are not necessary.

All the tools of differential geoemetry needed to the undersatanding of General Relativity will be carefully introduced and explained.

As well, some basics of Special Relativity will be given.

TEACHING METHODS

In presence

SYLLABUS/CONTENT

1. Fundations of General Relativity

• Pseudo-Riemannian geometry: manifolds, vector fields, connection, tensor, curvature, metric.
• Fundations of General Relativity: trajectories in a curved space-time, Einstein equations.

​2.  Solutions and applications

• Linearizzed theory
• Black hole spacetimes

RECOMMENDED READING/BIBLIOGRAPHY

 "General Relativity", C. Dappiaggi 

“Introduction to smooth manifold”, J. M. Lee  [per la geometria differenziale],

“Introduction to Riemannian manifold”, J. M. Lee  [per la geometria pseudo-riemanniana],

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

The class will start according to the academic calendar.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Oral exam.

ASSESSMENT METHODS

The oral exam will begin with a seminar presentation on a topic of your choice. It will then proceed to assess your understanding of the basic concepts of general relativity and your ability to manipulate the associated mathematical tools.

FURTHER INFORMATION

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.