Taught Courses
Covariant Physics and Black Hole Thermodynamics
Time: Fridays, 1pm to 2pm. Starts 17th September 2021.
Location: Lab 4 F15.
Online (Zoom): https://groups.oist.jp/quast/onlinecoursezoomaccess (login required)
Enrollment: https://groups.oist.jp/grad/specialtopicenrollmentapplication
Lecturers: Dr. Josh Kirklin, Dr. Isha Kotecha and Dr. Fabio Mele
Description: General covariance is one of the fundamental principles underlying gravity. It says that the laws of physics do not depend on our choice of coordinates. Geometrically speaking, this means that we can apply any diffeomorphism to a physical system without changing its properties. In other words, diffeomorphisms are a kind of gauge symmetry. In this course, we will explore an elegant modern perspective on general covariance, using an approach known as the covariant phase space formalism. This formalism tells you how to treat covariant theories using classical Hamiltonian mechanics. Quantum gravity must be a quantisation of this classical theory. This means that we can learn a lot about some aspects of the quantum theory using the covariant phase space approach. For example, the laws of black hole thermodynamics are a reflection of the fact that black holes are quantum objects. We will show how key fundamental thermodynamical properties of the black hole, such as its entropy, can be understood using the covariant phase space. We will also discuss more general properties of black hole thermodynamics. Finally, we will explore the connection between gauge symmetry and quantum entanglement, and how this relates to the thermodynamics of spacetime itself.
\(\mathrm{d}E = \frac{\kappa}{8\pi G}\mathrm{d}A + \Omega\,\mathrm{d}J+\Phi\,\mathrm{d}Q\)
Content:

Hamiltonian mechanics

Geometry of phase space, the symplectic form

Gauge symmetry and constraints in mechanics

Covariant field theories

Geometry of field space

Gauge symmetry and constraints in field theory

Global symmetries and large gauge symmetries

Conserved charges in general relativity

Black hole spacetimes and symmetries

Energy, angular momentum and electric charge

Black hole entropy as a Noether charge

The laws of black hole thermodynamics

Spacetime thermodynamics and the Einstein equations

Entanglement equilibrium and semiclassical Einstein equations

Entanglement and gauge symmetry
Notes:
See attachments below.
Recorded lectures:
Please click here for a list of all recorded lectures: https://web.microsoftstream.com/group/4f3192e2367a4246ad26b93a56dd2230?view=videos
References:
See in the notes attached below.