In more detail, the subjects are:
Series A: Aspects of low-dimensional quantum gravity. In these lectures I’ll give an overview of our current understanding of AdS_2 and AdS_3 quantum gravity. The lectures will discuss holographic properties of these theories and how it connects to physics of extremal and near-extremal black holes.
Series B: Non-relativistic gravity is the theory one obtains from the 1/c expansion of general relativity where c is the speed of light. This expansion can be done off shell and fully covariantly. I will show that the 1/c expansion can lead to two different classes of theories: strong and weak nonrelativistic gravity. The latter is Newtonian gravity (formulated in a covariant manner using Newton-Cartan geometry) plus its post-Newtonian corrections. The former is less well-known and includes effects such as time dilation in Newton-Cartan gravity. In the second part of the lectures we will focus on post-Newtonian expansions in the context of the classical problem of a compact radiating source of matter (which we will assume to be a perfect fluid). We will see that in this case the 1/c expansion has a finite region of validity and that it needs to be matched with an expansion in Newton's constant that is valid outside the compact matter source. This process is known as matched asymptotic expansion and we will discuss its essential features leading to a solution for the metric near the matter source and far away from it (where we measure the gravitational radiation).
Series A: Aspects of low-dimensional quantum gravity. In these lectures I’ll give an overview of our current understanding of AdS_2 and AdS_3 quantum gravity. The lectures will discuss holographic properties of these theories and how it connects to physics of extremal and near-extremal black holes.
Series B: Non-relativistic gravity is the theory one obtains from the 1/c expansion of general relativity where c is the speed of light. This expansion can be done off shell and fully covariantly. I will show that the 1/c expansion can lead to two different classes of theories: strong and weak nonrelativistic gravity. The latter is Newtonian gravity (formulated in a covariant manner using Newton-Cartan geometry) plus its post-Newtonian corrections. The former is less well-known and includes effects such as time dilation in Newton-Cartan gravity. In the second part of the lectures we will focus on post-Newtonian expansions in the context of the classical problem of a compact radiating source of matter (which we will assume to be a perfect fluid). We will see that in this case the 1/c expansion has a finite region of validity and that it needs to be matched with an expansion in Newton's constant that is valid outside the compact matter source. This process is known as matched asymptotic expansion and we will discuss its essential features leading to a solution for the metric near the matter source and far away from it (where we measure the gravitational radiation).
Series C: To understand the dynamics of black holes it is central to understand perturbations around the black hole space-time. This is introduced in a broader context, also related to the stability of black holes. Such perturbative phenomena includes quasi-normal modes, which are eigen modes that describe the dissipative oscillations of black holes in the ringdown process when perturbing it, as could happen in a process with colliding binary black holes. Another phenomena is superradiance, which is the enhancement of radiation in a Penrose like process where rotational energy is harvested from the black hole.
Each of the three series will start with a relevant background as well as an overview of recent developments. Subsequently the main topics will be discussed in-depth, including both technical details as well as the conceptual underpinnings. This will be done in part via pedagogical examples leading up to the state-of-the-art in the field. Exerciseses will be devised to illustrate and complement the course material, allowing the students to gain hands on experience with the new material. Each of the series will conclude with an overview of related subjects, open questions and important avenues for future research. The lectures and exercise sessions will be made as interactive as possible, ensuring there is time for questions and feedback.
Learning outcome
Knowledge:
The course introduces the student to modern ideas in gravity. This includes the black hole information paradox and how modern ideas such as holography can be employed to resolve the paradox. It includes also the dynamics of black holes, specifically concerning perturbations and instabilities. Finally, the student is introduced to modern ideas on a covariant formulation of non-relativistic gravity, which including a strong gravity regime extending Newton gravity with gravitational time-dilation effects.
Competences:
This course makes use of previously obtained knowledge in General Relativity, as well as certain modern methods of high-energy theory
such as holography and quantum field theory. The course gives the student the tools to be able to understand and contribute to the state-of-the-art developments in the field.
The course introduces the student to modern ideas in gravity. This includes the black hole information paradox and how modern ideas such as holography can be employed to resolve the paradox. It includes also the dynamics of black holes, specifically concerning perturbations and instabilities. Finally, the student is introduced to modern ideas on a covariant formulation of non-relativistic gravity, which including a strong gravity regime extending Newton gravity with gravitational time-dilation effects.
Competences:
This course makes use of previously obtained knowledge in General Relativity, as well as certain modern methods of high-energy theory
such as holography and quantum field theory. The course gives the student the tools to be able to understand and contribute to the state-of-the-art developments in the field.
Target group
Any PhD student interested in theoretical aspects of gravity. The PhD student should have a solid background in general relativity.
Teaching and learning methods
The lectures will be done using a blackboard since this format works well in theoretical courses. This allows for a relatively slow and pedagogical pace of the lectures, and for interactions between the students and the lecturer. In addition there will exercise sessions for the students, with theoretical exercises provided by the lecturers. There will be feedback from the lecturers both individually as well as collectively.
Lecturers
Prof. Alejandra Castro, Cambridge University, UK, will contribute by giving the lecture series A, along with theoretical exercises.
Prof. Oscar Dias, University of Southampton, UK, will contribute by giving the lecture series B, along with theoretical exercises.
Prof. Jelle Hartong, University of Edinburgh, UK, will contribute by giving the lecture series C, along with theoretical exercises.
Prof. Oscar Dias, University of Southampton, UK, will contribute by giving the lecture series B, along with theoretical exercises.
Prof. Jelle Hartong, University of Edinburgh, UK, will contribute by giving the lecture series C, along with theoretical exercises.
Workload
The course will start Monday morning, and end Friday at lunch time, so with lectures and theoretical exercises every day for 5 working days.
• Preparation: 25 hours
• Lectures: 30 hours
• Theoretical exercises: 15 hours
• Preparation: 25 hours
• Lectures: 30 hours
• Theoretical exercises: 15 hours
