Black Holes
| Code | School | Level | Credits | Semesters |
| MATH4016 | Mathematical Sciences | 4 | 20 | Spring UK |
- Code
- MATH4016
- School
- Mathematical Sciences
- Level
- 4
- Credits
- 20
- Semesters
- Spring UK
Summary
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 course uses techniques learnt in MATH4015 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.
Target Students
Single and Joint Honours students from the School of Mathematical Sciences. Mathematical Physics students. MSc students on the Gravity, Particles and Fields programme.
Classes
- Three 1-hour lectures each week for 11 weeks
Assessment
- 100% Exam 1 (3-hour): Written exam
Assessed by end of spring semester
Educational Aims
Thiscourse aims to introduce the physics of black holes and its mathematical description, giving insight into problems of research interest.Thiscourse is the last in a sequence of modules within the Relativity Pathway (MATH3018, MATH4015, MATH4016). Thecourse provides an opportunity to apply techniques and ideas learned in previous modules to important astrophysical problems. Students will acquire knowledge and skills to a level sufficient to begin research in general relativity.Learning Outcomes
A student who completes this course successfully should be able to:
L1 - demonstrate a clear understanding of the structure equations of a spherical perfect fluid star in general relativity and ways of solving them
L2 - explain the causal structure of black holes using different coordinate systems and conformal diagrams and give rigorous definitions of terms such as black hole, white hole, event horizon, killing horizon.
L3 - discuss the key features and properties of spherical, electrically charged black holes and rotating black holes and describe their role in astrophysics and cosmology.
L4 - perform calculations in relativistic spacetimes, including a collapsing star spacetime and black hole spacetimes, including frequency shifts, geodesic orbits, and dynamical processes involving ergoregions.
L5 - demonstrate a clear understanding of black hole mechanics and thermodynamics and of the role of Hawking radiation in the latter and as a stepping stone towards a quantum theory of gravity.