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A core-collapse supernova is generated by the passage of a shockwave throughthe envelope of a massive star, where the shock wave is initially launched fromthe ``bounce'' of the neutron star formed during the collapse of the stellarcore. Instead of successfully exploding the star, however, numericalinvestigations of core-collapse supernovae find that this shock tends to``stall'' at small radii ($\lesssim$ 10 neutron star radii), with stellarmaterial accreting onto the central object through the standing shock. Here, wepresent time-steady, adiabatic solutions for the density, pressure, andvelocity of the shocked fluid that accretes onto the compact object through thestalled shock, and we include the effects of general relativity in theSchwarzschild metric. Similar to previous works that were carried out in theNewtonian limit, we find that the gas ``settles'' interior to the stalledshock; in the relativistic regime analyzed here, the velocity asymptoticallyapproaches zero near the Schwarzschild radius. These solutions can representaccretion onto a material surface if the radius of the compact object isoutside of its event horizon, such as a neutron star; we also discuss thepossibility that these solutions can approximately represent the accretion ofgas onto a newly formed black hole following a core-collapse event. Ourfindings and solutions are particularly relevant in weak and failed supernovae,where the shock is pushed to small radii and relativistic effects are large.

Spherically Symmetric Accretion onto a Compact Object through a Standing Shock: The Effects of General Relativity in the Schwarzschild Geometry