In more detail, the subjects are:
Series A: To understand the quantum aspects of black holes is one of the holy grails of modern theoretical physics. This is about how to reconcile the macroscopic theory of general relativity with the microscopic theory of quantum physics, something which is still not clearly understood. This course will introduce the student to forefront developments in understanding the quantum structure of black holes and space-time. This includes the following topics: holography, entanglement entropy, island proposal and black hole microstate counting.
Series B: 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.
Series C: Recent developments show that non-relativistic gravity (NRG) can be studied in terms of a covariant, off-shell large speed of light expansion of general relativity, employing in particular a novel version of Newton-Cartan geometry. Depending on the matter content, the expansion either leads to Newton-Cartan geometry with absolute time or to Newton-Cartan geometry with non-relativistic gravitational time dilation effects. The latter shows that nonrelativistic gravity includes a strong field regime and goes beyond Newtonian gravity. Earlier work on Newton-Cartan geometry will be briefly discussed, after which modern approaches will be presented. Further topics include matter couplings, solutions and odd powers in 1/c, as well as the relation to of this new framework to Post-Newtonian expansion in GR. The lecture series concludes with a summary of related topics, such as the consideration of the opposite (small speed of light) limit and its relevance for astrophysical applications.
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.
Series A: To understand the quantum aspects of black holes is one of the holy grails of modern theoretical physics. This is about how to reconcile the macroscopic theory of general relativity with the microscopic theory of quantum physics, something which is still not clearly understood. This course will introduce the student to forefront developments in understanding the quantum structure of black holes and space-time. This includes the following topics: holography, entanglement entropy, island proposal and black hole microstate counting.
Series B: 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.
Series C: Recent developments show that non-relativistic gravity (NRG) can be studied in terms of a covariant, off-shell large speed of light expansion of general relativity, employing in particular a novel version of Newton-Cartan geometry. Depending on the matter content, the expansion either leads to Newton-Cartan geometry with absolute time or to Newton-Cartan geometry with non-relativistic gravitational time dilation effects. The latter shows that nonrelativistic gravity includes a strong field regime and goes beyond Newtonian gravity. Earlier work on Newton-Cartan geometry will be briefly discussed, after which modern approaches will be presented. Further topics include matter couplings, solutions and odd powers in 1/c, as well as the relation to of this new framework to Post-Newtonian expansion in GR. The lecture series concludes with a summary of related topics, such as the consideration of the opposite (small speed of light) limit and its relevance for astrophysical applications.
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, its consequences, 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.
Skills:
• The student should be able to understand the black hole information paradox and its consequences.
• The student should be able to apply holographic techniques to relate entanglement entropy to gravity.
• The student should understand the relevance of novel semiclassical saddle points of the gravitational path integral.
• The student should be able to understand the quasinormal spectrum of black holes.
• The student should be able to understand the superradiance instability of black holes.
• The student should be able to understand the equations for perturbations around black hole space-times.
• The student should be able to understand how Newton-Cartan geometry arises fromThe student should have a working understanding of the dynamics of non-relativistic gravity and its coupling to matter.
• The student should be familiar with some of the main applications of non-relativistic gravity to covariant formulation of Post-Newtonian physics as well as the strong gravity regime of General Relativity.
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, its consequences, 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.
Skills:
• The student should be able to understand the black hole information paradox and its consequences.
• The student should be able to apply holographic techniques to relate entanglement entropy to gravity.
• The student should understand the relevance of novel semiclassical saddle points of the gravitational path integral.
• The student should be able to understand the quasinormal spectrum of black holes.
• The student should be able to understand the superradiance instability of black holes.
• The student should be able to understand the equations for perturbations around black hole space-times.
• The student should be able to understand how Newton-Cartan geometry arises fromThe student should have a working understanding of the dynamics of non-relativistic gravity and its coupling to matter.
• The student should be familiar with some of the main applications of non-relativistic gravity to covariant formulation of Post-Newtonian physics as well as the strong gravity regime of General Relativity.
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
