The Blandford and Znajek (BZ) split-monopole serves as an important theoretical example of the mechanism that can drive the electromagnetic extraction of energy from Kerr black holes. It is constructed as a perturbative low spin solution of Force Free Electrodynamics (FFE). Recently, Armas et al. put this construction on a firmer footing by clearing up issues with apparent divergent asymptotics. This was accomplished by resolving the behavior around the outer light surface, a critical surface of the FFE equations. Building on this, we revisit the BZ perturbative expansion, and extend the perturbative approach to higher orders in the spin parameter of the Kerr black hole. We employ matched-asymptotic-expansions and semi-analytic techniques to extend the split-monopole solution to the sixth-order in perturbation theory. The expansion necessarily includes novel logarithmic contributions in the spin parameter. We show that these higher order terms result in non-analytic contributions to the power and angular momentum output. In particular, we compute for the first time the perturbative contributions to the energy extraction at seventh- and eighth-order in the spin parameter. The resulting formula for the energy extraction improves the agreement with numerical simulations at finite spin. Moreover, we present a novel numerical procedure for resolving the FFE equations across the outer light surface, resulting in significantly faster convergence and greater accuracy, and extend this to higher orders as well. Finally, we include a general discussion of light surfaces as critical surfaces of the FFE equations.
We consider force-free magnetospheres around the extreme Kerr black hole. In this case there is no known exact analytic solution to force free electrodynamics which is stationary, axisymmetric and magnetically-dominated. However, any stationary, axisymmetric and regular force-free magnetosphere in extreme Kerr black hole approaches the same attractor solution in the near-horizon extreme Kerr (NHEK) limit with null electromagnetic field. We show that by moving away from the attractor solution in the NHEK region, one finds magnetically-dominated solutions in the extreme Kerr black hole with finite angular momentum outflow. This result is achieved using a perturbative analysis up to the second order.
We propose a new approach to find magnetically-dominated force-free (FF) magnetospheres around highly spinning black holes, relevant for models of astrophysical jets. Employing the near-horizon extreme Kerr (NHEK) limit of the Kerr black hole, any stationary, axisymmetric and regular FF magnetosphere reduces to the same attractor solution in the NHEK limit with null electromagnetic field strength. We use this attractor solution as the universal starting point for perturbing away from the NHEK region in the extreme Kerr spacetime. We demonstrate that by going to second order in perturbation theory, it is possible to find magnetically dominated magnetospheres around the extreme Kerr black hole. Furthermore, we consider the near-horizon near-extreme Kerr (near-NHEK) limit that provides access to a different regime of highly spinning black holes. Also in this case we find a novel FF attractor, which can be used as the universal starting point for a perturbative construction of FF magnetospheres. Finally, we discuss the relation between the NHEK and near-NHEK attractors.
We formulate the theory of first-order dissipative magnetohydrodynamics in an arbitrary hydrodynamic frame under the assumption of parity-invariance and discrete charge symmetry. We study the mode spectrum of Alfvén and magnetosonic waves as well as the spectrum of gapped excitations and derive constraints on the transport coefficients such that generic equilibrium states with constant magnetic fields are stable and causal under linearised perturbations. We solve these constraints for a specific equation of state and show that there exists a large family of hydrodynamic frames that renders the linear fluctuations stable and causal. This theory does not require introducing new dynamical degrees of freedom and therefore is a promising and simpler alternative to Müller-Israel-Stewart-type theories. Together with a detailed analysis of transport, entropy production and Kubo formulae, the theory presented here is well suited for studying dissipative effects in various contexts ranging from heavy-ion collisions to astrophysics.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.