Spacetime constraints on accreting black holes

Abstract

We study the spin dependence of accretion onto rotating Kerr black holes using analytic techniques. In its linear regime, angular momentum transport in MHD turbulent accretion flow involves the generation of radial magnetic field connecting plasma in a differentially rotating flow. We take a first principles approach, highlighting the constraint that limits the generation and amplification of radial magnetic fields, stemming from the transfer of energy from mechanical to magnetic form. Because the energy transferred in magnetic form is ultimately constrained by gravitational potential energy or Killing energy, the spin dependence of the latter allows us to derive spin-dependent constraints on the success of the accreting plasma to expel its angular momentum. We find an inverse relationship between this ability and black hole spin. If this radial magnetic field generation forms the basis for angular momentum transfer in accretion flows, accretion rates involving Kerr black holes are expected to be lower as the black hole spin increases in the prograde sense.