[An easy one, ~ 10 min] Suppose gab and Fab is a solution to the
coupled system of Einstein's + Maxwell's equations for a certain physical
system. What is the equation of motion of a test body with mass m
and charge e in this space?
[Quantum gravity :) ~ 20 min] Estimate the Bohr radius of a gravitational
atom made of two neutrons bound by their gravitational attraction in
the lowest energy state.
[Now this is a hard one (just kidding), ~ 1 h] You have proved in
exercise 11 that a static solution (a'=a''=0) to Friedmann's equation does
exist if the cosmological constant is non-zero. Prove that this solution
is however unstable (assume that the universe is matter dominated).