Have you ever contemplated the reality of a black hole? How long does it take to create a black hole, or how much matter does it take, or how do you calculate its mass? Will our galaxy be consumed by a black hole? What would happen if you fell into a black hole? If you would like to know the answers to these questions, then this is the class for you.

This class is concerned with studying the effects that gravity has on the structure of spacetime, from length-scales starting around 10⁻¹³ cm (the radius of an elementary particle) up to around 10²⁸ cm (the radius of the universe). In order to understand these effects, we will use Einstein’s theory of relativity. Playing a fundamental role in our course will be the concept of a spacetime singularity – more precisely, a black hole. Thus, more precisely stated, this course will provide a direct examination of general relativity and black holes. However, instead of the typical approach, where one first learns the principles of relativity then, using them, proves the singularity theorems of Penrose and Hawking, we will go in the opposite direction. We will assume their existence and then, using the properties of non-spinning and spinning black holes, introduce Einstein’s theory.

Along the way, we will learn about the physics of flat spacetime (the special theory), curvature, metrics, tests of the general theory, the physics of black holes, cosmology, and gravitational waves, with other fascinating topics sprinkled throughout.

Throughout our development of the theory and its consequences, we will use only calculus and algebra, and require only the basics of Newtonian mechanics in order to achieve our goals. (While some basic knowledge of the special theory of relativity would be helpful, it is not a prerequisite). Class activities will consist of working through problems related to selected readings, alongside discussions, question/answer sessions; simulations (e.g galaxy creation, formation, and destruction); finding and analyzing numerical solutions to Einstein’s equations; and a few lectures.

This class will have weekly meetings via Zoom. These virtual assemblies will be used as a time for discussion of the topics from the readings, along with highlighting the problems and debating their solutions, as well as Q&A sessions.

In-person sessions will be used as time for students to present projects that they have worked through, guest presenters (on occasion), and ‘verification’ of the models to describe large-scale spacetime that we are learning about. In addition, we are hoping to be able to visit a nearby observatory where we can see the theories in action.

Prerequisites: If you are ready for AB Calculus exam, you are ready for this course.

About the Instructor

Kevin Wray – College Prep School
Kevin Wray has been teaching mathematics for the past six years at The College Preparatory School, and prior to that for four years at the University of California, Berkeley. Currently Kevin is teaching single variable calculus and multivariable calculus at CPS. He has also taught courses in linear algebra, abstract algebra, analysis, several seminars at Cal, as well as courses in classical mechanics, quantum physics, and relativity.

After finishing his undergrad, Kevin moved to Holland for a year as a member of the Mathematical Research Institute in Utrecht. He followed this by moving to Amsterdam, where he was a grad student in theoretical physics at the Universiteit van Amsterdam. After completing his degree at the UvA, Kevin moved to Berkeley for work as a graduate student in mathematics. Upon completion at Cal, Kevin started work at The College Preparatory School.

Kevin enjoys taking hikes, bike rides, surfing, really pretty much anything outdoors, basketball, olympic-style weightlifting, and, of course, reading math and physics papers and books.