Vacuum and nonvacuum black holes in a uniform magnetic field

Azreg‐Aïnou, Mustapha

doi:10.1140/epjc/s10052-016-4259-6

Cited by 29 publications

(34 citation statements)

References 51 publications

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“…The constraints, ∂ θ F 4 ∝ sin n θ or 0 and ∂ θ F 5 ∝ sin n θ or 0 with n ≥ 1, ensure that the expressions of F tν ;ν and F ϕν ;ν have finite limits as θ → 0 or π (on the axis of rotation). Note that the ansatz (6) to (9) is conform to the different available expressions [8,16,20,21] for F µν due to the presence of a magnetic field B asymptotically parallel to the axis of symmetry.…”

Section: B the Electromagnetic Fieldmentioning

confidence: 92%

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Epicyclic oscillations of charged particles in stationary solutions immersed in a magnetic field with application to the Kerr–Newman black hole

Azreg‐Aïnou

2019

Int. J. Mod. Phys. D

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We consider a stationary metric immersed in a uniform magnetic field and determine general expressions for the epicyclic frequencies of charged particles. Applications to the Kerr-Newman black hole is reach of physical consequences and reveals some new effects among which the existence of radially and vertically stable circular orbits in the region enclosed by the event horizon and the so-called "innermost" stable circular orbit in the plane of symmetry. I. WHY STUDYING AND DETERMINING THE EPICYCLIC OSCILLATIONS (ECOS)?Any small deviations from a stable, geodesic or nongeodesic, motion lead to an epicyclic motion around the stable path. If the epicyclic motion is that of a charged particle, the corresponding frequencies have direct observational effects [1]- [5].The general non-circular motion of charged particles in the geometry of a magnetized Schwarzschild black hole has been investigated [6] without, however, dealing with the epicyclic oscillations (ECOs). The easiest motion where ECOs may be determined analytically is the circular one [7], from this point of view ECOs of charged particles around circular paths of the Kerr black hole have been studied and their frequencies were determined in terms of the parameters of the black hole, the weak magnetic field in which it is immersed, the charged particle physical properties, and the fourvelocity vector of the circular geodesic motion [8,9]. One of the purposes of the present work is to determine the frequencies of the ECOs of charged particles around circular paths of a general stationary solution immersed in a magnetic field then apply them to the case of the Kerr-Newman black hole immersed in a magnetic field.In Sec. II we set the ansatz for the metric and electromagnetic field of a stationary metric immersed in a uniform magnetic field. In Sec. III we derive general expressions for the epicyclic frequencies and in Sec. IV we discuss some properties of the perturbed circular motion. In Sec. V we apply our results to the case of the Kerr-Newman black hole immersed in a magnetic field. We conclude in Sec. VI. II. THE METRIC AND THE ELECTROMAGNETIC FIELDWe split this section into two subsections dealing with the rotating charged metric, with charge Q, and the linear form of the resulting electromagnetic field due to the interaction of the charge Q with a uniform magnetic field B. A. The metricUsing the required symmetry properties of a stationary and axisymmetric spacetime that is circular [10] -a spacetime admitting the existence of two commuting 1 Killing vectors, a timelike one ξ µ t = (1, 0, 0, 0) and a spacelike one ξ 1 In a circular spacetime, there exists a family of two surfaces everywhere orthogonal to the plane defined by the two commuting Killing vectors ξ µ t and ξ µ ϕ . In such a spacetime one may choose the coordinates such that the only nonzero cross term of the metric is dtdϕ.

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Section: B the Electromagnetic Fieldmentioning

confidence: 92%

“…As has been emphasized in [16], Wald's formula applies only to the Schwarzschild and Kerr black holes where…”

Section: A the Metric And Electromagnetic Fieldmentioning

confidence: 99%

Epicyclic oscillations of charged particles in stationary solutions immersed in a magnetic field with application to the Kerr–Newman black hole

Azreg‐Aïnou

2019

Int. J. Mod. Phys. D

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“…Following the arguments in Ref. [60] we generalize our solution (27) by introducing a Kerr-like metric which describes a rotating wormhole in BEC dark matter halo. The metric has the following form…”

Section: A Kerr-like Metric For Rotating Wormholesmentioning

confidence: 99%

On the possibility of wormhole formation in the galactic halo due to dark matter Bose–Einstein condensates

2019

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It has been recently claimed that dark matter could be in the form of a Bose-Einstein condensate (BEC) in order to explain the dynamics at large distances from the galactic center [Boehmer, Harko, JCAP 0706, 025 (2007)]. In this paper we explore the possibility of wormhole formation in galactic halos due to the dark matter BEC. In particular we have found a new wormhole solution supported by BEC dark matter using the expressions for the density profile of the BEC and rotation velocity along with the Einstein field equations to calculate the wormhole red shift function as well as the shape function. To this end, we show that for a specific choose of the central density of the condensates our wormhole solution satisfies the flare our condition. Furthermore we check the null, weak, and strong condition at the wormhole throat with a radius r 0 , and shown that in general the energy condition are violated by some arbitrary quantity at the wormhole throat. Using the volume integral quantifier, and choosing reasonable values of parameters we have calculate the amount of BEC exotic matter near the wormhole throat, such that the wormhole extends form r 0 to a a cut off radius situated at 'a . Moreover we have introduced a Kerr-like metric for a rotating BEC wormhole to study the effect of BEC dark matter on the Lense-Thirring precession frequencies. Namely, we have shown that the obtained precession frequencies lie within a range of typical quasi-periodic oscillations (QPOs).

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“…However, the inequalities in (2) are supposed to hold in the regions of the three-space where the Killing vector ξ µ t is timelike. It is straightforward to show that ω is the angular velocity of the zero-angular-momentum observers (ZAMOs) [17]. We choose a reference frame (e t , e r , e θ , e φ ) dual to the 1-forms defined in (3):…”

Section: A Zero-angular-momentum Observersmentioning

confidence: 99%

“…In equations (20) and (21), u t is given by (17) and it diverges by (13) as the fluid approaches a horizon. One of the factors in each of Eq.…”

Section: A Flow In the Vicinity Of The Horizonsmentioning

confidence: 99%

Accretion of rotating fluids onto stationary solutions

Azreg‐Aïnou

2017

Phys. Rev. D

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We consider a general stationary solution and derive the general laws for accretion of rotating perfect fluids. For non-degenerate and degenerate Fermi and Bose fluids we derive new effects that mimic the center-of-mass-energy effect of two colliding particle in the vicinity of horizons. Nondegenerate fluids see their chemical potential grow arbitrarily and ultra-relativistic Fermi fluids see their specific enthalpy and Fermi momentum grow arbitrarily too while the latter vanishes gradually for non-relativistic Fermi fluids. For degenerate Bose fluids two scenarios remain possible as the fluid approaches a horizon: a) The Bose-Einstein condensation ceases or b) the temperature drops gradually down to zero. The critical flow is also investigated. I. WHAT IS ACCRETION?Given a metric solution of spacetime, a geodesic motion is the process by which a massive or massless test particle "falls" freely. The fall motion may be bounded (circular motion or else) or unbounded (scattering motion). The free fall of the test particle does not disturb, affect, or modify the given geometry: No back reaction effects are taken into consideration. Moreover, no group motion is treated in geodesic motion. Back reaction effects are present in the calculation of gravitational self forces where the motion of the "small" body is still seen as geodesic in the perturbed metric.Accretion is an advanced state of motion. It describes group motion with and without back reaction and it is generally non-geodesic. By group motion it is meant that the accreting matter is modeled by a fluid and that each fluid element encompasses a) a sufficiently large number of particles to be described statistically by an average pressure, average temperature, average particle number density, and average energy density; b) a sufficiently small number of particles compared to the whole system (accreting matter, atmosphere, etc). These conditions are easily met in astrophysics and atmospheric motion. The presence of a gradient of pressure, which is a sort of fluid group self force, renders the accretion motion non-geodesic.In accretion motion back reaction effects are taken into consideration in numerical and simulation analyses [1][2][3]. Full analytical treatments [4-8] drop back reaction effects for simplicity and cognitive treatments [9-15] may include emission effects and neglect back reaction too.All the above-mentioned treatments make common simplificative physical assumptions of symmetry concerning both the given background geometry and the fluid. They assume the background metric to remain stationary and time-independent during accretion [16]. The analysis remains valid for accretion time, larger than free-fall time, and much smaller than the ratio mass/(mass rate change) of the star.In this work we will keep using the standard set of simplificative assumptions to describe the accretion of rotating perfect fluids onto rotating black holes with no back reaction or emission effects. In Sec. II we present the accretion model and in sec. III we derive the gen...

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Vacuum and nonvacuum black holes in a uniform magnetic field

Cited by 29 publications

References 51 publications

Epicyclic oscillations of charged particles in stationary solutions immersed in a magnetic field with application to the Kerr–Newman black hole

Epicyclic oscillations of charged particles in stationary solutions immersed in a magnetic field with application to the Kerr–Newman black hole

On the possibility of wormhole formation in the galactic halo due to dark matter Bose–Einstein condensates

Accretion of rotating fluids onto stationary solutions

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