## Admission Requirements

BSc physics, BSc astronomy, BSc mathematics. An introductory bachelor course in gravity such as the "Introduction to general relativity and astrophysical applications" offered in Leiden is strongly recommended.

## Description

The classical theory of gravity can be interpreted as the geometry of space-time.It combines the language of field theory with the language of differential geometry onmanifolds. The basic concepts of these subjects will be introduced and it will be shown how they are used to describe gravitational phenomena, from relativistic corrections to orbits of planets and stars, to gravitational waves, black holes and the evolution of the universe at large.

Topics:

Review of newtonian gravity

Review of Special Relativity

Differential geometry on manifolds, including the concepts of metric, connection and curvature

Equivalence principle, geodesic motion

Einstein equations, variational principle

Gravitational waves

Schwarzschild solution, stars and black holes

Cosmology of a homogeneous and isotropic universe

## Course objectives

This course provides the basis for work in relativistic astronomy, cosmology, quantum gravity and applications. It will :

acquaint you with the concepts of field theory and differential geometry

teach you to use these concepts to solve problems of gravitational physics and cosmology

prepare you for advanced courses on gravitational physics and cosmology

allow you to access the scientific literature on these topics and understand the recent progress in experimental and observational research

## Timetable

## Mode of instruction

Class room lectures will introduce the material. Homework problems are provided to practice mathematical methods and gain experience in their application to gravitational physics.

## Assessment method

A midterm and a final written exam will together determine the grading of the course, the weight of the midterm exam being 40% and of the final exam 60% of the final grade.

## Blackboard

Course material is on Blackboard.

To have access to Blackboard you need a ULCN-account.Blackboard UL

## Reading list

Primary text book:

S. Carroll, Spacetime and Geometry, an Introduction to General Relativity (Benjamin Cummings, 2003).

Recommended background reading:

J.B. Hartle, an introduction to Einstein's general relativity, (Addison-Wesley, 2003). A bachelor level introductory text stressing the physical concepts.

R. Wald, General Relativity (Univ. Chicago Press, 1984). High level treatise of the relevant differential geometry.

C. Misner, K. Thorne, J.A. Wheeler, Gravitation (Freeman, 1973). Standard text on the professional level

## Contact

Lecturer: Prof.dr.A. Achucarro(Ana