Backreaction of the Mass and Angular Momentum Accretion on Black Holes: General Formulation and Application to the Blandford-Znajek Process
2021
We study the backreaction of the mass and angular momentum accretion on black
holes. We first develop the formalism of monopole and dipole linear
gravitational perturbations around the Schwarzschild black holes in the
Eddington-Finkelstein coordinates against the generic time-dependent matters.
We derive the relation between the time dependence of the mass and angular
momentum of the black hole and the energy-momentum tensors of accreting
matters. As a concrete example, we apply our formalism to the Blandford-Znajek
process around the slowly rotating black holes. We find that the time
dependence of the monopole and dipole perturbations can be interpreted as the
slowly rotating Kerr metric with time-dependent mass and spin parameters, which
are determined from the energy and angular momentum extraction rates of the
Blandford-Znajek process. We also show that the Komar angular momentum and the
area of the apparent horizon are decreasing and increasing in time,
respectively, while they are consistent with the Blandford-Znajek argument of
energy extraction in term of black hole mechanics if we regard the
time-dependent mass parameter as the energy of the black hole.
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