Context. We investigate the deposition of energy and momentum due to the annihilation of neutrinos (ν) and antineutrinos (ν) in the vicinity of steady, axisymmetric accretion tori around stellar-mass black holes (BHs). This process is widely considered as an energy source for driving ultrarelativistic outflows with the potential to produce gamma-ray bursts. Aims. We analyze the influence of general relativistic (GR) effects in combination with different neutrinosphere properties on the νν-annihilation efficiency and spatial distribution of the energy deposition rate. Methods. Assuming axial symmetry, we numerically compute the annihilation rate 4-vector. For this purpose, we construct the local neutrino distribution by ray-tracing neutrino trajectories in a Kerr space-time using null geodesics. We vary the value of the dimensionless specific angular momentum a of the central BH, which provides the gravitational field in our models. We also study different shapes of the neutrinospheres, spheres, thin disks, and thick accretion tori, whose structure ranges from idealized tori to equilibrium non-selfgravitating matter distributions. Furthermore, we compute Newtonian models where the influence of the gravitational field on the annihilation process is neglected. Results. Compared to Newtonian calculations, GR effects increase the total annihilation rate measured by an observer at infinity by a factor of two when the neutrinosphere is a thin disk, but the increase is only ≈25% for toroidal and spherical neutrinospheres. Comparing cases with similar luminosities, thin disk models yield the highest energy deposition rates by νν-annihilation, and spherical neutrinospheres the lowest ones, independently of whether GR effects are included. Increasing a from 0 to 1 enhances the energy deposition rate measured by an observer at infinity by roughly a factor of 2 due to the change of the inner radius of the neutrinosphere. General relativity and rotation cause important differences in the spatial distribution of the energy deposition rate by νν-annihilation.Key words. gamma rays: bursts -neutrinos -accretion, accretion disks -relativity -black hole physics -stars: neutron IntroductionIt is widely believed that systems powering gamma-ray bursts (GRB) could be newborn, stellar-mass black holes (BHs) accreting matter at hyper-critical rates (up to several solar masses per second) from a surrounding accretion disk with a mass of some hundredth of a solar mass up to possibly a solar mass (see, e.g., Piran 2005). These central engines may form in a "collapsar" event where the core of a massive, rotating Wolf-Rayet star collapses to a BH and the accretion of the stellar envelope may eventually lead to a GRB-supernova event with relativistic mass ejection along the rotation axis (Woosley 1993;MacFadyen & Woosley 1999;Aloy et al. 2000). Accreting BHs may also be the remnants of mergers of two compact objects in close binaries (Eichler et al. 1989;Mochkovitch et al. 1993). In the first scenario the system is embedded in the enve...

We present the first stationary, axisymmetric neutron star models with meridional circulation in general relativity. For that purpose, we developed generally rotating neutron star, a new code based on a fixedpoint iteration. We find a two-dimensional set of meridional circulation modes, which differ by the number of vortices in the stream lines of the neutron star fluid. For expected maximal meridional circulation velocities of about 1000 km=s, the vortices cause surface deformations of about a percent. The deformations depend on the shape of the vortices close to the surface and increase with the meridional circulation velocity. We also computed models of rotating neutron stars with meridional circulation, where neither the surface rotates nor does the rotation velocity exceed the circulation velocity.