organized by the Max Planck Institute for Gravitational Physics (Albert Einstein Institute).

**March 2 – 13, 2020**

The Max Planck Institute for Gravitational Physics (Albert Einstein Institute) offers a crash course on General Relativity, Black Holes and Gravitational-Wave Astrophysics. This course can be attended by students studying from the 5th semester Physics or Mathematics.

The spring school will first introduce general relativity; we will then discuss black holes and neutron stars; the final section will be about gravitational waves, and will cover in particular the recent discoveries of merging black holes and neutron stars which were awarded the 2017 Nobel Prize of Physics. Our institute was involved in these discoveries, and we also give insights into current research at the institute, both related to gravitational waves and beyond.

Lectures will take place daily during the morning. In the afternoons, we provide exercises and the opportunity for questions and discussions. We also plan two excursions to sights in the vicinity of Potsdam.

The 20th Jürgen Ehlers Spring School takes place at the Max Planck campus in Potsdam. Potsdam is the capital of the state of Brandenburg and hosts multiple UNESCO World-Heritage Sites. It lies in close proximity to Berlin.

Information on how to get to the Max Planck campus in Potsdam can be found here.

## Address

Max Planck Institute for Gravitational Physics

Am Mühlenberg 1

14476 Potsdam

## Contact

## Application

Application to the 20th Jürgen Ehlers Spring School can be submitted via our online portal until December 8, 2019. We aim to notify successful applicants by December 20, 2019.

The number of participants is limited to 40.

## Prerequisites

A working knowledge of introductory university physics (classical mechanics, electromagnetism), and mathematics (advanced calculus, linear algebra) will be assumed. Some prior exposure to differential geometry is desirable but not required.

## Abstracts

### Week 1: Introduction to General relativity and the theory of black holes

The first week’s lectures will be devoted to the study of Einstein’s theory of General Relativity and the theoretical foundations for black holes and neutron stars.

### Week 2: Gravitational Wave astronomy

This week will mainly give an overview of gravitational wave astronomy. Topics include the theory of gravitational waves and a discussion of the major astrophysical sources of gravitational waves, most notably inspiraling compact object binaries (i.e. black holes or neutron stars). After an exposition of gravitational wave detectors and an introduction to gravitational wave data-analysis, the recent spectacular observations of gravitational waves by the LIGO/Virgo detectors will be treated.

## Schedule

### Week 1

Mon | Tue | Wed | Thu | Fri | |||||

9:15 – 10:45 | General Relativity Jeremie Joudioux, Ignacio Reyes | General Relativity Jeremie Joudioux, Ignacio Reyes | General Relativity Jeremie Joudioux, Ignacio Reyes | General Relativity Jeremie Joudioux, Ignacio Reyes | Black Holes Ana Alonso Serrano | ||||

11:00 – 12:30 | General Relativity Jeremie Joudioux, Ignacio Reyes | General Relativity Jeremie Joudioux, Ignacio Reyes | General Relativity Jeremie Joudioux, Ignacio Reyes | General Relativity Jeremie Joudioux, Ignacio Reyes | Black HolesAna Alonso Serrano | ||||

Lunch | |||||||||

14:00 – 15:30 | Exercises | Exercises | Excursion Einstein Haus Caputh (tbc) | Exercises | Quantum puzzles & BH Ro Jefferson | ||||

15:45 – 17:15 | Exercises | Exercises | Excursion Einstein Haus Caputh (tbc) | Exercises | |||||

evening | Reception | ||||||||

### Week 2

9:15 – 10:45 | Cosmology Jean-Luc Lehners | Gravitational Waves Deyan Mihaylov | Gravitational Waves Deyan Mihaylov | LIGO/Virgo observations Abhirup Ghosh | LISA Jonathan Gair | ||||

11:00 – 12:30 | Cosmology Jean-Luc Lehners | Gravitational Waves Deyan Mihaylov | LIGO/Virgo observations Abhirup Ghosh | LIGO/Virgo observations Abhirup Ghosh | Supergravity in a nutshell Franz Ciceri | ||||

Lunch | |||||||||

14:00 – 15:30 | Exercises | Exercises |
| Exercises | Alternative theories of gravity Robert Benkel | ||||

15:45 – 17:15 | Exercises | Exercises |
| Exercises | |||||

evening |

## Complementary Reading

### Introduction to general relativity and the theory of black holes

- Schutz, B., A first course in General Relativity
- Hartle, Gravity: An Introduction to Einstein’s General Relativity

### Gravitational waves

- Flanagan, E., Hughes, S., The Basics of Gravitational Wave Theory http://adsabs.harvard.edu/abs/2005NJPh….7..204F
- The basic physics of the binary black hole merger GW150914 https://arxiv.org/abs/1608.01940
- B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Observation of Gravitational Waves from a Binary Black Hole Merger, https://arxiv.org/abs/1602.03837 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.061102

## Organizers

- Enrico Brehm
- Kenta Kiuchi
- Harald Pfeiffer