OVERVIEW

The course is part of the first semester of the 1st/2nd year of the Master’s Degree in Physics. It is part of the curriculum of a theoretical physicist. The subject is characterized by an important mathematical structure, which in this course is considered as a necessary tool to deepen the physical contents of General Relativity.

AIMS AND CONTENT

LEARNING OUTCOMES

An overview of Einstein’s theory of gravitational interactions, including its main implications and applications.

AIMS AND LEARNING OUTCOMES

The course provides an introduction to Einstein’s theory of General Relativity. No preliminary mathematical course is required, but only familiarity with covariant formalism and the principles of field theory (action, equations of motion as functional derivatives of action versus fields). The minimum differential geometry tools needed to construct the Einstein-Hilbert action and deduce Einstein equations as field equations will be introduced. The main purpose of the course is to transmit to the student the rich physical content of Einstein’s equations: black holes, gravitational waves and an introduction to cosmology

TEACHING METHODS

lectures at blackboard (60h)

SYLLABUS/CONTENT

•    Manifolds
    ◦    Gravity as geometry
    ◦    What is a manifold?
    ◦    Vectors again
    ◦    Tensors again
    ◦    The metric
    ◦    An expanding universe
    ◦    Causality
    ◦    Tensor densities

•    Curvature
    ◦    Overview
    ◦    Covariant derivatives
    ◦    Parallel transport and geodesics
    ◦    Properties of geodesics
    ◦    The expanding universe revisited
    ◦    The Riemann curvature tensor
    ◦    Properties of the Riemann tensor
    ◦    Symmetries and Killing vectors
    ◦    Maximally symmetric spaces

•    Gravitation
    ◦    Physics in curved spacetime
    ◦    Einstein’s equation
    ◦    Lagrangian formulation
    ◦    Properties of Einstein’s equation
    ◦    The cosmological constant

•    The Schwarzschild Solution
    ◦    The Schwarzschild metric
    ◦    Birkhoff’s theorem
    ◦    Singularities
    ◦    Geodesics of Schwarzschild
    ◦    Experimental tests
    ◦    Schwarzschild black holes
    ◦    Stars and black holes

•    More General Black Holes
    ◦    The black hole zoo
    ◦    Event Horizons
    ◦    Killing Horizons
    ◦    Mass, charge, and spin
    ◦    Charged (Reissner-Nordström) black holes
    ◦    Rotating (Kerr) black holes

•    Perturbation Theory and Gravitational Radiation
    ◦    Linearized theory and gauge transformations
    ◦    Degrees of freedom
    ◦    Newtonian fields and photon trajectories
    ◦    Gravitational wave solutions

•    Cosmology
    ◦    maximally symmetric universes
    ◦    Robertson-Walker metrics
    ◦    the Friedmann equations
    ◦    evolution of the scale factor
    ◦    redshifts and distances
    ◦    gravitational lensing
    ◦    our universe
    ◦    inflation

RECOMMENDED READING/BIBLIOGRAPHY

• Sean M. Carroll: Spacetime and Geometry: An Introduction to General Relativity
• James B. Hartle: Gravity: An Introduction to Einstein’s General Relativity
• Ta-Pei Cheng: Relativity, Gravitation and Cosmology: A Basic Introduction

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

september 21, 2026

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The written test concerns a simple application of the contents presented during the course. It consists of a single exercise to be carried out in one hour.

ASSESSMENT METHODS

The written test concerns a simple application of the contents presented during the course. It consists of a single exercise to be carried out in one hour. The oral exam is organized as follows. The student is offered an entry from the course lesson register, and is given a few minutes to organize a lesson on the assigned topic lasting approximately 30 minutes, during which the members of the commission can ask related questions.

FURTHER INFORMATION

Compensatory and dispensatory measures Disability/Invalidity/Specific Learning Disorder

Dispensatory measures and compensatory tools are intended to enable students to achieve the same learning objectives as their fellow students, not to facilitate the examination.

The use of compensatory tools and the application of dispensatory measures must be authorised in advance by the teacher in agreement with the Referee.

To take advantage of the adaptations during the examination, fill in the Adaptation request form; the request will be automatically sent by the system to the teacher in charge of the teaching, to the Contact Person of your School/Area/Department and in copy to the Sector; you will also receive a copy of the request sent by e-mail.

The adjustments available to students are as follows:

• Additional time (+30% DSA)
• Additional time (+50% disability/invalidity)
• Additional time during oral exams to organise the answer
• Calculator (programmable and graphing calculators are not allowed)
• Conceptual Maps
• Tables and/or Forms
• Take the exam in written form
• Take the exam in oral form
• Tutor reader (for written tests only)
• Tutor-writer (for written tests only)

Your request for adaptations must be submitted at least 7 working days before the scheduled exam date.

All information for students with disabilities and DSA is available on the webpage: Services for students with disabilities or DSA | UniGe | University of Genoa

Reference for inclusion: Sergio Di Domizio - sergio.didomizio@unige.it