Can neutrinos from neutron star mergers power gamma-ray bursts?

We perform three-dimensional hydrodynamical simulations of the coalescence of binary neutron stars. We include the emission and backreaction of gravitational waves into the Newtonian ``Piecewise Parabolic Method''. The use of the physical equation of state of Lattimer & Swesty (1991) allows us to take into account the production of neutrinos. We evaluate our models for the efficiency of neutrino-antineutrino annihilation in the surroundings of the coalescing neutron stars. The corresponding energy deposition prior to and during merging turns out to be 2--3 orders of magnitude too small to power a typical gamma-ray burst with an energy output of about 10^{51}/(4 pi) erg/sterad at cosmological distances. Analytical estimates of the subsequent evolution of the disk which possibly surrounds the central black hole show that even under the most favorable conditions the energy in a fireball of electron-positron pairs and photons that is created by neutrino-antineutrino annihilation falls short by at least an order of magnitude.