  Like-charged macroions attract each other as a result of strong electrostatic
correlations in the presence of multivalent counterions or at low temperatures.
We investigate the effective electrostatic interaction between i) two
like-charged rods and ii) two like-charged spheres using the recently
introduced strong-coupling theory, which becomes asymptotically exact in the
limit of large coupling parameter (i.e. for large counterion valency, low
temperature, or high surface charge density on macroions). Since we deal with
curved surfaces, an additional parameter, referred to as Manning parameter, is
introduced, which measures the ratio between the radius of curvature of
macroions to the Gouy-Chapman length and controls the counterion-condensation
process that directly affects the effective interactions. For sufficiently
large Manning parameters (weakly-curved surfaces), we find a strong long-ranged
attraction between two macroions that form a closely-packed bound state with
small surface-to-surface separation of the order of the counterion diameter in
agreement with recent simulations. For small Manning parameters (highly-curved
surfaces), on the other hand, the equilibrium separation increases and the
macroions unbind from each other as the confinement volume increases to
infinity. This occurs via a continuous universal unbinding transition for two
charged rods at a threshold Manning parameter of 2/3, while the transition is
discontinuous for spheres because of a pronounced potential barrier at
intermediate distances.
