A new method is presented for finding Killing tensors in spacetimes with symmetries. The method is used to find all the Killing tensors of Melvins magnetic universe and the Schwarzschild vacuum. We show that they are all trivial. The method requires
less computation than solving the full Killing tensor equations directly, and it can be used even when the spacetime is not algebraically special.
We investigate the doping of a geometrically frustrated spin ladder with static holes by a complementary approach using exact diagonalization and quantum dimers. Results for thermodynamic properties, the singlet density of states, the hole-binding en
ergy and the spin correlations will be presented. For the undoped systems the ground state is non-degenerate, with translationally invariant nearest-neighbor spin correlations. In the doped case, we find that static holes polarize their vicinity by a localization of singlets in order to reduce the frustration. This polarization induces short range repulsive forces between two holes and an oscillatory behavior of the long range two-hole energy. For most quantities investigated, we find very good agreement between the quantum dimer approach and the results from exact diagonalization.
