28. one point, from Lecture 28, short answer, some pictures, time consuming

(a) .3 Defining Open and Closed Universes. Define ``open'' and ``closed'' and ``just on the boundary'' universes in terms of expansion (draw this, relating it to a one-dimensional hyperbola, circle, and parabola), the curvature R, the mass density T, the mass density parameterOmega, and the total energy of the universe. There are 15 pieces of information here. (.1 for every 5 correct answers.)

(b) .3 Interesting Dead Stars. There are three end results for a ``dead'' star: a white dwarf, a neutron star, and a black hole. Say what each is in terms of initial mass relative to the mass of the sun, core mass relative to the mass of the sun, and final size (a length, not a mass). (.1 for every 3 correct answers.)

(c) .1 Defining a Black Hole. Characterize a black hole in terms of T, R, time, the path of light. (.1 if all four are right.)

(d) .2 Seeing Dark Things. How do we observe black holes (.1) and dark matter? (.1) Use a picture or two if you need to.

Revised October 26, 1997.