  Massive stars are usually found in binaries, and binaries with periods less
than 10 days may have a preference for near equal component masses. In this
paper we investigate the evolution of these binaries all the way to contact and
the possibility that these systems can be progenitors of double neutron star
binaries. The small orbital separations of observed double neutron star
binaries suggest that the progenitor systems underwent a common envelope phase
at least once during their evolution. Bethe & Brown (1998) proposed that
massive binary twins will undergo a common envelope evolution while both
components are ascending the red giant branch or asymptotic giant branch
simultaneously, also known as double-core evolution. Using models generated
from the stellar evolution code Evolve Zero Age Main Sequence, we determine the
range of mass ratios resulting in both components simultaneously ascending the
RGB or AGB as a function of the difference in birth times, t. We find that,
even for a generous t=5 Myr, the minimum mass ratio qmin=0.933 for an 8 Solar
Mass primary and increases for larger primaries. We use a hydrodynamics code,
StarSmasher, to study specifically the evolution of q=1 common envelope systems
as a function of initial component mass, age, and orbital separation. We find
the dynamical stability limit, the largest orbital separation where the binary
becomes dynamically unstable, as a function of the component mass and age.
Finally, we calculate the efficiency of ejecting matter during the inspiral
phase to extrapolate the properties of the remnant binary from our numerical
results, assuming the common envelope is completely ejected. We find that for
the nominal core masses, there is a minimum orbital separation for a given
component mass such that the helium cores survive common envelope evolution in
a tightly bound binary and are viable progenitors for double neutron stars.
