Table of contents
Course description
A quantitative overview of the mechanics of black holes and a qualitative
introduction to concepts from the theory of general relativity. Topics include
classical orbits; causality, spacetime, and spacetime curvature; orbits around
non-spinning black holes; angular momentum in curved spacetime; gravitational
wave astronomy; and black hole interiors. Students will also explore numerical
integration, data analysis, and signal processing techniques using the
programming language
python-3.7.
Learning goals
By the end of this course, students should expect to know or be able to do the following:
- The concepts underlying general relativity in broad strokes (not necessarily its mathematical details)
- An intuition for the basic physics of black holes, as laid out within the framework of general relativity
- Implement data analysis and numerical simulation algorithms using Python
Instructor information
| Cosmic address | Alex Urban 131 Carr Hall Allegheny College Meadville, PA, USA |
Planet Earth Sol stellar system Milky Way galaxy Virgo Supercluster |
aurban1@lsu.edu |
This is the best way to reach me | |
| Office hours | Tuesday, Thursday 10-11:30 AM | Other times available by request |
| Class meeting time | Wednesday, Friday 08-08:50 AM 107 Carr Hall |
Coffee/tea and light snacks provided by French Creek Coffee and Tea Co. |
Grading
This course is offered on a binary Credit / No Credit basis. In practice, this amounts to the following:
- Black hole astrophysics is a complicated enough subject at this stage of your career without the hassle of intense scrutiny, looming deadlines, and all that sort of nonsense
- As such, there will be no graded homeworks, quizzes, or exams, and absolutely no final exam of any kind
- You should think of this as akin to on-the-job training: receiving two credits will largely be based on attendance and in-class participation
Every week of the course will be united by a common theme
(see the table below).
Each Wednesday and Friday will feature a classic-style lecture in which I
present a deep dive into a different aspect of black holes or general
relativity. Each Monday we will have optional sessions in which studnets work
on a guided project related to the previous week's theme.
These projects will almost always involve either numerical simulation or
data analysis techniques, which we will learn to use via the programming
language python-3.7. In this way, you should expect to get
an overall sense of where the field of black hole astrophysics stands
today, and what your work experience would be if you chose to pursue
that line of study.
Accessibility
- This course is committed to an inclusive teaching style in which everyone is welcome to contribute.
- If you have suggestions that would improve the class environment, please don't hesitate to reach out
Semester schedule
This schedule is subject to change for pacing reasons and/or to provide better
projects. Please check back roughly each Monday to see what will be covered in
class that week.
| Week | Theme | Wednesday topic(s) | Friday topic(s) |
|---|---|---|---|
| 1 | A time for introductions | 15 Jan Course and syllabus overview Differential equations, symmetry, and constants of motion Gravitation and Kepler's laws |
17 Jan Escape velocity and the nature of orbits Orbital equations of motion, the effective radial potential Introduction to Python |
| 2 | What time is it on Mars? | 22 Jan Motion in the center-of-mass reference frame Physics of the effective radial potential Bound and unbound orbits, conic sections |
24 Jan Tidal forces, the Roche potential, and the speed of gravity Euler's method, trapezoid rule, and the RK4 method Simulating two-body classical orbits |
| 3 | Time and relative dimension in space | 29 Jan Spacetime and causality The relativity of simultaneity Time dilation, length contraction, and "paradoxes" |
— |
| 4 | In which things get very strange | 5 Feb Relativistic Doppler effect Aberration of light Ultra-relativistic astrophysics: γ-ray bursts |
7 Feb The curvature of spacetime Local flatness and the equivalence principle Are space and time really curved? |
| 5 | In which things get very heavy | 12 Feb Geometric types of curvature Spacetime coordinates and tangent spaces Tensors and the spacetime metric |
14 Feb The metric tensor Einstein field equations Special topic: is grad school right for me? |
| 6 | The easy things are hard | 19 Feb Geodesics and parallel transport Metric connection and covariant derivative Stress-energy tensor |
21 Feb Solving the Einstein field equations Schwarzschild metric: the "simplest nontrivial solution" Symmetry and conserved quantities |
| 7 | Cutting it close, or: black holes do not suck | 26 Feb Birkhoff's theorem Gravitational time dilation Special cases and null geodesics |
28 Feb Gravitational lensing in broad strokes Apsidal precession and timelike geodesics Black hole capture orbits |
| 8 | Space and time... are spinning? | 4 Mar Innermost stable circular orbit (ISCO) Photon scattering and black hole shadows Visualizing a gravitational plunge |
6 Mar Spin angular momentum in curved spacetime The ergosphere, superradiance, and the Penrose process Inner and outer horizons |
| 9 | Gravitational waves | 11 Mar Oblate spheroidal coordinates and the ring singularity Linearized gravity and gravitational radiation Tidal forces and gravitational wave detectors |
13 Mar Tidal forces and gravitational waves The gravitational wave spectrum Global network of ground-based detectors |
| 10 | Spring break | 18 Mar — |
20 Mar — |
| 11 | COVID-19 (out)break | 25 Mar — |
27 Mar — |
| 12 | Our worldlines, re-converged | 1 Apr Social distancing check-in Ground-based gravitational wave detectors Source constraints from Kepler's 3rd law |
3 Apr Multimessenger astronomy The astrophysics of compact binary merger Inferring source properties from gravitational waves |
| 13 | In which space becomes time and calamity ensues | 8 Apr Tidal forces and spaghettification Approaching the event horizon, from two reference frames Radial null geodesics, advanced and delayed time |
10 Apr Charting a better map: Kruskal-Szekeres coordinates White holes, black holes, and singularities Visualizing causality with Carter-Penrose diagrams |
| 14 | Actual time travel, and other broken rules | 15 Apr Rotating black holes: inner and outer horizons Ring singularities and the Cauchy surface Parallel universes (but don't read too much into it) |
17 Apr Hydrostatic equilibrium and stellar interiors Nuclear fusion, degeneracy pressure, equations of state Physical black hole formation, gravitational collapse |
| 15 | All good things... | 22 Apr Gravitational wave signatures of black hole formation "Realistic" black hole interiors, null singularities Quantum gravity: things general relativity cannot say |
24 Apr 1,000 ways to die from a black hole |