Remember to show all calculations and always include a complete, clear explanation of your reasoning.

• 1. Wald, Problem 9.2.
   
• 2. Comoving observers in FLRW spacetime: Consider the congruence of comoving observer worldlines in a Friedmann-Lemaître-Robertson-Walker spacetime with scale factor a(t), where t is the proper time for a comoving observer. Determine whether the worldlines are geodesics, and find the expansion, shear and twist of the congruence. Find out under what conditions the singularity theorem 9.5.1 in Wald's book applies to this spacetime, and if it does, state what the conclusion is.
   
• 3. Static observers in Kerr spacetime: Consider the congruence of static observer worldlines (observers at fixed r, \(\theta\) and \(\phi\)) in a Kerr spacetime of mass M and rotation parameter a. Determine whether the worldlines are geodesics, and find the expansion, shear and twist of the congruence.