TOPICS IN GENERAL RELATIVITY
Einstein's Theory of General Relativity can be summarized in three words: Matter curves spacetime. In this course, we'll learn what at least two of those words, curvature and spacetime, mean. The course will begin with a quick treatment of surfaces in three dimensions followed by a crash course in special relativity. We will then proceed to learn about the Riemann, Ricci, and Einstein curvature tensors in order to discuss the Einstein Equation, G = 8 pi T. We will study explicit solutions to the Einstein Equation like the Minkowski, Schwarzschild, and Vaidya spacetimes, which respectively represent vacuum, a static black hole, and black hole formation. We will also discuss the Big Bang, dark energy, the shape of the universe, and topics related to dark matter. Other topics will depend on the questions asked by the students. The target audience for this course are graduate students and undergraduate mathematics majors who are confident in their math skills. Students should be very good at multivariable calculus and linear algebra to take this course. However, we will not assume students already know differential geometry.