On the quasiblack-hole limit of rotating charged fluids

Abstract

We investigate the extremal quasiblack-hole (QBH) limit of stationary, axisymmetric charged perfect fluids in rigid or differential rotation, with and without pressure. We emphasize Weyl-type configurations, whose redshift factor is functionally related to the generalized electromagnetic potential. In this limit, the redshift factor vanishes throughout the fluid interior and the boundary becomes a quasihorizon. We require regular matter and electromagnetic fields and smooth matching to the exterior. Under suitable convergence assumptions, electromagnetic regularity and the approach to uniform rotation imply a constant generalized electromagnetic potential throughout the connected fluid interior, independently of the Weyl ansatz. With additional integrability conditions, the mass formula reduces to the extremal Kerr-Newman Smarr relation. For rigid rotation, we examine charged dust obeying a linear Weyl relation and fluids with pressure obeying the Kloster-Das or Guilfoyle relations. The linear Kloster-Das subclass becomes pressureless in the limit, whereas the general Guilfoyle case allows nonzero pressure. The Islam ansatz obstructs a regular limit when its coupling parameter, limiting potential, and limiting charge density are nonzero. For differential rotation, we analyze configurations with an identically vanishing Lorentz-force term and a linear Weyl subclass whose regularity requires control of angular-velocity gradients. Our results show that rotating Weyl-type systems admit extremal QBH limits much like their static counterparts, extending analyses of rotating dust distributions and identifying conditions for more general rotating charged fluids to be compatible with this limit.