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In this note we observe that the exact Maxwell-Einstein equations in the background metric of a spinning string can be solved analytically. This allows us to construct an analytical model for the magnetosphere which is approximately force free near to the spinning string. As in the case of a Kerr black hole in the presence of an external magnetic field the spinning string will acquire an electric charge which depends on the vorticity carried by the spinning string. The self-generated magnetic field and currents strongly resemble the current and magnetic field structure of the jets associated with active galaxies as they emerge from the galactic center.
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We consider the evolution of a cosmic string loop that is captured by a much more massive and compact black hole. We show that after several reconnections that produce ejections of smaller loops, the loop that remains bound to the black hole moves on a nearly-periodic non-self-intersecting trajectory, the orbit. The orbit evolves due to an energy and angular momentum exchange between the loop and the spinning black hole. We show that such evolution is mathematically equivalent to a certain continuous deformation of an auxiliary closed curve in a 3-dimensional space; for zero black-hole spin this deformation is curve-shortening that has been extensively studied by mathematicians. The evolution features competing effects of loop growth by the superradiant extraction of the black-hole spin energy, and loop decay by the friction of the moving string against the horizon. A self-intersection of an auxiliary curve corresponds to a capture by the black hole of a new string segment and thus an addition of a new captured loop. Possible asymptotic states of such evolution are shown to be strong emitters of gravitational waves. Whether reconnections prevent reaching the asymptotic states remains to be explored. Additionally, the orbits shape also evolves due to an emission of gravitational waves, and a recoil of the black hole that changes the orbit and likely leads to self-intersections. We argue that for a significant range of the dimensionless tension $mu$, string loops are captured by supermassive black holes at the centers of galaxies. This strongly motivates further study of interaction between string loops and black holes, especially the influence of this process on the black hole spindown and on the production of gravitational waves by strings created in galactic nuclei. We also discuss potential loop captures by primordial black holes.
We performed one-dimensional force-free magnetodynamic numerical simulations of the propagation of Alfven waves along magnetic field lines around a spinning black-hole-like object, the Banados--Teitelboim--Zanelli black string, to investigate the dynamic process of wave propagation and energy transport with Alfven waves. We considered axisymmetric and stationary magnetosphere and perturbed the background magnetosphere to obtain the linear wave equation for the Alfven wave mode. The numerical results show that the energy of Alfven waves monotonically increases as the waves propagate outwardly along the rotating curved magnetic field line around the ergosphere, where energy seems not to be conserved, in the case of energy extraction from the black string by the Blandford--Znajek mechanism. The apparent breakdown of energy conservation suggests the existence of an additional wave induced by the Alfven wave. Considering the additional fast magnetosonic wave induced by the Alfven wave, the energy conservation is recovered. Similar relativistic phenomena, such as the amplification of Alfven waves and induction of fast magnetosonic waves, are expected around a spinning black hole.
Soft Gamma-Ray Repeaters and Anomalous X-Ray Pulsars are extreme manifestations of the most magnetized neutron stars: magnetars. The phenomenology of their emission and spectral properties strongly support the idea that the magnetospheres of these astrophysical objects are tightly twisted in the vicinity of the star. Previous studies on equilibrium configurations have so far focused on either the internal or the external magnetic field configuration, without considering a real coupling between the two fields. Here we investigate numerical equilibrium models of magnetized neutron stars endowed with a confined twisted magnetosphere, solving the general relativistic Grad-Shafranov equation both in the interior and in the exterior of the compact object. A comprehensive study of the parameters space is provided to investigate the effects of different current distributions on the overall magnetic field structure.
Quantum electrodynamics (QED) effects may be included in physical processes of magnetar and pulsar magnetospheres with strong magnetic fields. Involving the quantum corrections, the Maxwell electrodynamics is modified to non-linear electrodynamics. In this work, we study the force-free magnetosphere in non-linear electrodynamics in a general framework. The pulsar equation describing a steady and axisymmetric magnetosphere is derived, which now admits solutions with corrections. We derive the first-order non-linear corrections to the near-zone dipole magnetosphere in some popular non-linear effective theories. The field lines of the corrected dipole tend to converge on the rotational axis so that the fields in the polar region are stronger compared to the pure dipole case.
As is well known, gravitational wave detections of coalescing binaries are standard sirens, allowing a measurement of source distance by gravitational wave means alone. In this paper we explore the analogue of this for continuous gravitational wave emission from individual spinning neutron stars, whose spin-down is driven purely by gravitational wave emission. We show that in this case, the distance measurement is always degenerate with one other parameter, which can be taken to be the moment of inertia of the star. We quantify the accuracy to which such degenerate measurements can be made. We also discuss the practical application of this to scenarios where one or other of distance or moment of inertia is constrained, breaking this degeneracy and allowing a measurement of the remaining parameter. Our results will be of use following the eventual detection of a neutron star spinning down through such gravitational wave emission.
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