Offered every winter term.

## Brief description:

Einstein's theory of general relativity, proposed in 1916, is the currently accepted theory of gravity. It has superseded Newton's theory of gravity, since it satisfies all experimental and observational tests, whereas Newton's theory does not.

Einstein's theory has led to a number of dramatic predictions. Firstly, it predicts that a sufficiently massive star will eventually undergo gravitational collapse and form a black hole, an object whose gravitational attraction is so strong that light cannot escape from it. Secondly, it predicts the existence of gravitational waves, which are emitted when massive objects undergo rapid accelerations (e.g. binary systems containing a neutron star). Thirdly, when the theory is applied on the largest possible scales, namely to the universe as a whole (the subject of cosmology) it predicts that the universe is expanding and that it originated in a cosmic explosion approximately 20 billion years ago. There is strong observational support for the first and third predictions, but so far gravitational waves have not been detected (current detectors are not sufficiently sensitive).

The goal of the course is to give an introduction to Einstein's theory of general relativity, culminating in a discussion of the simplest type of black hole, the Schwarzshild black hole, and of the simplest cosmological model, the Friedmann-Lematre model. The differential geometry and tensor analysis that is needed to formulate the theory will be developed in the first part of the course.

## Intended audience:

AMATH majors, Physics majors and other undergraduates who are interested in finding out about general relativity. Graduate students interested in undertaking research in general relativity. The course will provide a sound foundation for future work (graduate students should enroll in AMATH 675, and will be required to do extra work).

## Prerequisite background:

AMATH 231 and AMATH 261/PHYS 263. Fourth year standing is required since the course will require an appropriate level of maturity.