We use models of rapidly rotating neutron stars in general relativity
to construct evolutionary tracks for the recycling of pulsars to milli
second periods. We give an exact treatment for a simple recycling scen
ario where accretion occurs from the inner edge of a Keplerian disk on
to a bare neutron star. For this scenario we tabulate the shortest ach
ievable period and corresponding accreted rest mass for 13 nuclear equ
ations of state. For each equation of state, we determine whether a no
nrotating 1.4 M. star can be spun up to millisecond periods without ex
ceeding the maximum mass or rotation limits. We find that spin-up is p
ossible for all of the equations of state, even those with a static ma
ximum mass close to 1.4 M..