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With the goal of providing more accurate and realistic estimates of thesecular behavior of the mass accretion and drag rates in the "common-envelope"scenario encountered when a black hole or a neutron star moves in the stellarenvelope of a red supergiant star, we have carried out the first generalrelativistic simulations of the accretion flow onto a nonrotating black holemoving supersonically in a medium with regular but different density gradients.The simulations reveal that the supersonic motion always rapidly reaches astationary state and it produces a shock cone in the downstream part of theflow. In the absence of density gradients we recover the phenomenology alreadyobserved in the well-known Bondi--Hoyle--Lyttleton accretion problem, withsuper-Eddington mass accretion rate and a shock cone whose axis is stablyaligned with the direction of motion. However, as the density gradient is madestronger, the accretion rate also increases and the shock cone is progressivelyand stably dragged toward the direction of motion. With sufficiently largegradients, the shock-cone axis can become orthogonal to the direction, or evenmove in the upstream region of the flow in the case of the largest densitygradient. Together with the phenomenological aspects of the accretion flow, wehave also quantified the rates of accretion of mass and momentum onto the blackhole. Simple analytic expressions have been found for the rates of accretion ofmass, momentum, drag force, and bremsstrahlung luminosity, all of which havebeen employed in the astrophysical modelling of the secular evolution of abinary system experiencing a common-envelope evolution...

Common-envelope Dynamics of a Stellar-mass Black Hole: General Relativistic Simulations