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We compute the evolution of a quasi-spherical, slowly rotating accretion flowaround a black hole, whose mass and spin evolve adequately to the mass-energytransfer through the horizon. Our model is relevant for the central enginedriving a long gamma ray burst, that originates from the collapse of a massivestar. The computations of a GRB engine in a dynamically evolving spacetimemetric are important specifically due to the transient nature of the event, inwhich a huge amount of mass is accreted and changes the fundamental black holeparameters, its mass and spin, during the process. We discuss the results inthe context of angular momentum magnitude of the collapsing star. We also studythe possible formation and evolution of shocks in the envelope, which maytemporarily affect accretion. Our results are important for the limitations onthe mass and spin range of black holes detected independently byelectromagnetic observations of GRBs and gravitational waves. We speculate onthe possible constraints for the final masses and spins of these astrophysicalblack holes. It is shown that the most massive BHs were rahter not formed in apowerful GRB explosion, if the cores of their progenitors were only weaklyrotating.

Accretion in a dynamical spacetime and spinning up of the black hole in the gamma ray burst central engine