Jan 22-May 03, 2019
Credit: 3 graduate
Instructor(s): Tsunefumi Tanaka

Course Description

Registration begins on October 29th - please register for CRN 33552.
What do we mean by "curved spacetime"? As you freely fall toward a black hole, how long does it take to reach the event horizon according to your watch? Can your friend at a safe distance actually see you cross the horizon? What happens at the horizon? Can you receive messages and packages from your friend on the outside? Can you send messages to your friend on the outside? How quickly will it be over at the central crunch point?

You can answer these questions for yourself with some math, starting from a simple formula, the "metric," for the black hole. You can also answer every possible question about trajectories of light and satellites around the black hole as well as around familiar centers of gravitational attraction such as the Earth and Sun. Also, there is the metric describing the entire universe. The metric tells us how the universe expands and ends.

SYLLABUS: The course begins by examining the idea of spacetime curvature and the Schwarzschild metric for a non-rotating black hole. With the metric we calculate the circumferences of circles in space around a large mass and find they do not match up with their radii in the usual way. As in special relativity, we find that observers disagree in startling ways, but general relativity even puts limits on our ability to construct reference frames in which to study these effects. We will calculate the consequence of spacetime curvature outside and inside a Schwarzschild black hole, Hawking radiation, and rotating black holes. We will learn the Big Bang, forms of energy driving the expansion of the universe, and cosmological models.

NOTE: Participants should have good math skills, especially in calculus. They should know how to find a maximum and a minimum of a function and should be able to integrate polynomial functions. Also, participants need to be familiar with quantization of light energy (Planck relation), Heisenberg uncertainty principle, time dilation, length contraction, relativistic energy, and other basic principles in modern physics. Some knowledge of astronomy would be helpful.

Meeting Place and Times

Teachers log into the course at a time of day that best fits their schedule. It is necessary to connect at least 4 - 6 times per week and spend 9 - 12 hours each week while the course is in session, either online or offline working on course related assignments, to stay current and successfully complete this 3 credit graduate course.


Tsunefumi Tanaka, PhD. After graduating from Montana State University in 1997, I taught physics and astronomy at universities in Virginia and California for 9 years before moving to New Zealand. Now back in the US, I have been teaching at the University of Puget Sound in Tacoma, WA. I chose a career in physics because of my early interest in black holes, astrophysics, and cosmology, although my doctoral thesis was actually in quantum field theory. I enjoy typical geeky stuff such as SciFi, computers, and aquarium. I also enjoy cycling, hiking, and fishing, and I am also an avid amateur astronomer. I use my own telescopes and one in the UPS Observatory to gaze stars. I miss the clear sky in Montana, as we have too many rainy nights in Tacoma.


One year of College Physics; Differential & Integral Calculus; an Introductory Modern Physics course is preferred but as long as participants are familiar with basic principles of modern physics they should be okay; and Special Relativity such as the NTEN course SPECIAL RELATIVITY.

Target Audience

This course is designed primarily for high school science teachers.

Time Commitment:

9-12 hours per week. If you are unfamiliar with this field of study and/or method of delivery, you may require more time.

Tuition and Fees

If you are accepted into a qualified online program, see the appropriate MSU Online Only Tuition and Fee table below:

If you are also taking a face-to-face course, please refer to the MSU Fee Schedules.

Teachers are responsible for purchasing the required text(s) for the course on their own. They are listed below.

Required Books/Materials

  • An Introduction to Modern Cosmology, 3rd Ed.
    Author: Andrew Liddle
    Publisher: Wiley
    ISBN-10: 1118502140
    ISBN-13: 978-1118502143
    Under $35 in paperback or eTextbook
  • Exploring Black Holes: Introduction to General Relativity, 2nd Ed.
    Author: Taylor, Edwin F.; Wheeler, John Archibald
    You can download Exploring Black Holes from the author's website - free download.

Teacher/participants are responsible for obtaining the required texts for the course on their own before the course begins.

Computer Requirements:

  • Internet access
  • A device and browser that pass the system check for Brightspace LE, MSU's learning management system.

This course uses a learning management system. You will learn more closer to the course start date.

For More Information

For questions regarding registration, please contact Kelly Boyce by phone at (800)282-6062 or (406)994-6812, or by email at

For questions regarding course content, please contact Tsunefumi Tanaka at

How to Register

You must be accepted as a student to Montana State University to take this course.

Learn how to apply.

After your application has been accepted, you will register via MSU's online registration system, MyInfo.

Registration requires a PIN number. Learn how to find your PIN.

Once you have your PIN, learn how to register through MyInfo.