Black hole in a uniform magnetic field
TL;DR: In this paper, the authors derived the solution for the electromagnetic field occurring when a stationary, axisymmetric black hole is placed in an originally uniform magnetic field aligned along the symmetry axis of the black hole.
Abstract: Using the fact that a Killing vector in a vacuum spacetime serves as a vector potential for a Maxwell test field, we derive the solution for the electromagnetic field occurring when a stationary, axisymmetric black hole is placed in an originally uniform magnetic field aligned along the symmetry axis of the black hole. It is shown that a black hole in a magnetic field will selectively accrete charges until its charge becomes $Q=2{\mathrm{Bb}}_{0}J$, where ${B}_{0}$ is the strength of the magnetic field and $J$ is the angular momentum of the black hole. As a by-product of the analysis given here, we prove that the gyromagnetic ratio of a slightly charged, stationary, axisymmetric black hole (not assumed to be Kerr) must have the value $g=2$.
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TL;DR: In this paper, the authors argue that coupling the Abelian Higgs model to gravity plus a negative cosmological constant leads to black holes which spontaneously break the gauge invariance via a charged scalar condensate slightly outside their horizon.
Abstract: I argue that coupling the Abelian Higgs model to gravity plus a negative cosmological constant leads to black holes which spontaneously break the gauge invariance via a charged scalar condensate slightly outside their horizon. This suggests that black holes can superconduct.
1,378 citations
Cites background from "Black hole in a uniform magnetic fi..."
...It has long been understood that extremal black holes can exhibit perfect diamagnetism [9, 10, 11], but the reasons for it are essentially geometrical, whereas the proposals of [1] and of the current paper focus on a charged scalar condensate that develops slightly outside the horizon of non-extremal black holes....
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TL;DR: In this paper, a new numerical code, ECHO, based on an Eulerian Conservative High Order scheme for time dependent three-dimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD), is presented.
Abstract: We present a new numerical code, ECHO, based on an Eulerian Conservative High Order scheme for time dependent three-dimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD). ECHO is aimed at providing a shock-capturing conservative method able to work at an arbitrary level of formal accuracy (for smooth flows), where the other existing GRMHD and GRMD schemes yield an overall second order at most. Moreover, our goal is to present a general framework, based on the 3+1 Eulerian formalism, allowing for different sets of equations, different algorithms, and working in a generic space-time metric, so that ECHO may be easily coupled to any solver for Einstein's equations. Various high order reconstruction methods are implemented and a two-wave approximate Riemann solver is used. The induction equation is treated by adopting the Upwind Constrained Transport (UCT) procedures, appropriate to preserve the divergence-free condition of the magnetic field in shock-capturing methods. The limiting case of magnetodynamics (also known as force-free degenerate electrodynamics) is implemented by simply replacing the fluid velocity with the electromagnetic drift velocity and by neglecting the matter contribution to the stress tensor. ECHO is particularly accurate, efficient, versatile, and robust. It has been tested against several astrophysical applications, including a novel test on the propagation of large amplitude circularly polarized Alfven waves. In particular, we show that reconstruction based on a Monotonicity Preserving filter applied to a fixed 5-point stencil gives highly accurate results for smooth solutions, both in flat and curved metric (up to the nominal fifth order), while at the same time providing sharp profiles in tests involving discontinuities.
295 citations
Cites methods from "Black hole in a uniform magnetic fi..."
...D test in a curved space-time we consider the equilibrium force-free solution found by Wald (1974), here in Schwarzschild metric....
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TL;DR: In this paper, a new numerical code, ECHO, based on a Eulerian conservative high-order scheme for time dependent three-dimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD), is presented.
Abstract: Aims. We present a new numerical code, ECHO, based on a Eulerian conservative high-order scheme for time dependent three-dimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD). ECHO is aimed at providing a shock-capturing conservative method able to work at an arbitrary level of formal accuracy (for smooth flows), where the other existing GRMHD and GRMD schemes yield an overall second order at most. Moreover, our goal is to present a general framework based on the 3+1 Eulerian formalism, allowing for different sets of equations and different algorithms and working in a generic space-time metric, so that ECHO may be easily coupled to any solver for Einstein's equations. Methods. Our finite-difference conservative scheme previously developed for special relativistic hydrodynamics and MHD is extended here to the general relativistic case. Various high-order reconstruction methods are implemented and a two-wave approximate Riemann solver is used. The induction equation is treated by adopting the upwind constrained transport (UCT) procedures, appropriate to preserving the divergence-free condition of the magnetic field in shock-capturing methods. The limiting case of magnetodynamics (also known as force-free degenerate electrodynamics) is implemented by simply replacing the fluid velocity with the electromagnetic drift velocity and by neglecting the contribution of matter to the stress tensor. Results. ECHO is particularly accurate, efficient, versatile, and robust. It has been tested against several astrophysical applications, like magnetized accretion onto black holes and constant angular momentum thick disks threaded by toroidal fields. A novel test of the propagation of large-amplitude , circularly polarized Alfven waves is proposed, and this allows us to prove the spatial and temporal high-order properties of ECHO very accurately. In particular, we show that reconstruction based on a monotonicity-preserving (MP) filter applied to a fixed 5-point stencil gives highly accurate results for smooth solutions, both in flat and curved metric (up to the nominal fifth order), while at the same time providing sharp profiles in tests involving discontinuities.
280 citations
TL;DR: In this article, the authors investigated the possibility that gamma-ray bursts are powered by a central engine consisting of a black hole with an external magnetic field anchored in a surrounding disk or torus.
256 citations
TL;DR: In this paper, a complex charged scalar coupled to a Reissner-Nordstr?m black hole in 3+1 dimensional anti-de Sitter spacetime was studied.
Abstract: We study a system of a complex charged scalar coupled to a Reissner-Nordstr?m black hole in 3+1 dimensional anti-de Sitter spacetime, neglecting back-reaction. With suitable boundary conditions, the cases of a neutral and purely electric black hole have been studied in various limits and were shown to yield key elements of superconductivity in the dual 2+1 dimensional field theory, forming a condensate below a critical temperature. By adding magnetic charge to the black hole, we immerse the superconductor into an external magnetic field. We show that a family of condensates can form and we examine their structure. For finite magnetic field, they are localized in one dimension with a profile that is exactly solvable, since it maps to the quantum harmonic oscillator. As the magnetic field increases, the condensate shrinks in size, which is reminiscent of the Meissner effect.
237 citations
Cites background from "Black hole in a uniform magnetic fi..."
...In particular, if the effective mass (1)The fact that certain black holes and branes are known to exhibit a sort of Meissner effect[5, 6, 7] at zero temperature has always added to the motivation, although it has not been clear how exactly this could be connected to a dual superconductivity....
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