  We discuss head-on collisions of neutron stars and disks of dust ("galaxies")
following the ideas of equilibrium thermodynamics, which compares equilibrium
states and avoids the description of the dynamical transition processes between
them. As an always present damping mechanism, gravitational emission results in
final equilibrium states after the collision. In this paper we calculate
selected final configurations from initial data of colliding stars and disks by
making use of conservation laws and solving the Einstein equations. Comparing
initial and final states, we can decide for which initial parameters two
colliding neutron stars (non-rotating Fermi gas models) merge into a single
neutron star and two rigidly rotating disks form again a final (differentially
rotating) disk of dust. For the neutron star collision we find a maximal energy
loss due to outgoing gravitational radiation of 2.3% of the initial mass while
the corresponding efficiency for colliding disks has the much larger limit of
23.8%.
