This module will develop the ideas behind General Relativity (GR) to an advanced level. You will explore solutions to these equations including black holes and cosmological solutions.
You will also have the opportunity to study more advanced topics including modified gravity models (eg models with extra dimensions) that are at the forefront of current research.
General relativity predicts the existence of black holes which are regions of space-time into which objects can be sent but from which no classical objects can escape. This module develops techniques to systematically study black holes and their properties, including horizons and singularities. Astrophysical processes involving black holes are discussed, and there is a brief introduction to black hole radiation discovered by Hawking.
The modern study of general relativity requires familiarity with a number of tools of differential geometry, including manifolds, symmetries, Lie Groups, differentiation and integration on manifolds. These are introduced in this module using examples of curved space-times.
This module provides an introduction to the modern theory of gravitation: Einstein's general theory of relativity.
Topics to be covered include:
- Specifying geometry
- Special Relativity
- Equivalence principle
- General relativity
- Schwarzschild solution
- Schwarzschild black hole:
Gravity, Particles and Fields Dissertation
The dissertation is an extended piece of research related to a taught element of the course. The study will be largely self-directed, with oversight and input provided where necessary by a supervisor from the School of Mathematical Sciences or the School of Physics and Astronomy.
The topic could be based on a theoretical investigation, a review of research literature, or a combination of the two.
Introduction to Quantum Information Science
The paradigm of Quantum Information Science (QIS) is that quantum devices, made of systems such as atoms and photons, can out-perform the present-day technology in key applications ranging from computing power and communication security to precision measurements. Quantum information processing and the measurement and control of individual quantum systems are central topics in QIS, lying at the intersection of quantum mechanics with 'classical' disciplines such as information theory, probability, and statistics, computer science and control engineering.
The aim of this module is to provide an introduction to QIS, emphasising the differences and similarities between the classical and the quantum theories. After a short review of the necessary probabilistic notions, the first part introduces the operational framework of quantum theory involving the fundamental concepts of states, measurements, quantum channels, instruments. This includes some of the influential results in the field such as entanglement and quantum teleportation, Bell's theorem and the quantum no-cloning theorem. The second part covers at least two topics from quantum Markovian evolutions, quantum statistics, continuous variable systems.
This module facilitates an understanding of Friedmann models and hot big bang – encompassing the study of thermal history, freezout, relics, recombination, last scattering; dark matter candidates.
Other topics will include inflation, fluctuations from inflation, structure formation, gravitational lensing CMB anisotropies, and dark energy.
Quantum Field Theory
The aim of this module is to provide the quantum description of electrons, photons and other elementary particles, including a discussion of spin, bosons, and fermions.
Lectures will provide an introduction to functional integrals, Feynman diagrams, and the standard model of particle physics.