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- Find the laws of transformation of light-cone coodinate under a boost and give the expression of proper time in terms of these coodinates.
- Show that the functions that define the generalised Bogolyubov transform must have a wronskian equal to i to conserve the algebra of creation and annihilation operators.
- What is the time dependence of conformal time in a radiation-dominated universe and in a matter-dominated universe? What is the value of conformal time today? At what value of the conformal time did the cosmic microwave background decouple ([math]z=1000[/math])?
- Calculate (in K) the Hawking temperature of a 1-solar-mass black hole. How large should the acceleration of an observer be for the corresponding Unruh temperature to be 300 K?