Static Axially Symmetric Gravitational Fields

Voorhees, Burton

doi:10.1103/physrevd.2.2119

Cited by 253 publications

(227 citation statements)

References 5 publications

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“…These are the prolate Zipoy-Voorhees (ZV) solutions [29,50]. Unless for λ 2 = 1 they are not spherically symmetric and exhibit a curvature singularity at R = x = m. These metrics have been relatively well studied, as they can be used to describe deformations of the Schwarzschild black hole (see for example [51,52]).…”

Section: Prolate Vacuum Metricsmentioning

confidence: 99%

Weyl metrics and wormholes

Gibbons

Volkov

2017

J. Cosmol. Astropart. Phys.

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Abstract. We study solutions obtained via applying dualities and complexifications to the vacuum Weyl metrics generated by massive rods and by point masses. Rescaling them and extending to complex parameter values yields axially symmetric vacuum solutions containing singularities along circles that can be viewed as singular matter sources. These solutions have wormhole topology with several asymptotic regions interconnected by throats and their sources can be viewed as thin rings of negative tension encircling the throats. For a particular value of the ring tension the geometry becomes exactly flat although the topology remains non-trivial, so that the rings literally produce holes in flat space. To create a single ring wormhole of one metre radius one needs a negative energy equivalent to the mass of Jupiter. Further duality transformations dress the rings with the scalar field, either conventional or phantom. This gives rise to large classes of static, axially symmetric solutions, presumably including all previously known solutions for a gravity-coupled massless scalar field, as for example the spherically symmetric Bronnikov-Ellis wormholes with phantom scalar. The multi-wormholes contain infinite struts everywhere at the symmetry axes, apart from solutions with locally flat geometry.arXiv:1701.05533v3 [hep-th]

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Section: Prolate Vacuum Metricsmentioning

confidence: 99%

Weyl metrics and wormholes

Gibbons

Volkov

2017

J. Cosmol. Astropart. Phys.

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“…With the perturbation (21) and conditions (14) and (19), the perturbed conservation equations (18) can be written in explicit form as…”

Section: B Thin Disk Casementioning

confidence: 99%

“…Furthermore, the superposition of black holes with static disks were analyzed by Lemos and Letelier [10,11,12] and Klein [13]. Bičák and Ledvinka [14] found relativistic counter-rotating thin disks as sources of Kerr type metrics, and Bičák, LyndenBell and Katz [15] obtained static disks as sources of known vacuum spacetimes from the Chazy-Curzon metric [16,17] and Zipoy-Voorhees metric [18,19], also Bičák, Lynden-Bell and Pichon [20] found an infinite number of new static solutions. Recently, exact solutions for thin disks with single and composite halos of matter [21], thin disks made of charged dust [22], thin disks made of charged perfect fluid [23], and thick disks [24] were obtained.…”

Section: Introductionmentioning

confidence: 99%

Stability of general relativistic geometric thin disks

Ujevic

Letelier

2004

Phys. Rev. D

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The stability of general relativistic thin disks is investigated under a general first order perturbation of the energy momentum tensor. In particular, we consider temporal, radial and azimuthal "test matter" perturbations of the quantities involved on the plane z = 0. We study the thin disks generated by applying the "displace, cut and reflect" method, usually known as the image method, to the Schwarzschild metric in isotropic coordinates and to the Chazy-Curzon metric and the ZipoyVoorhees metric (γ-metric) in Weyl coordinates. In the case of the isotropic Schwarzschild thin disk, where a radial pressure is present to support the gravitational attraction, the disk is stable and the perturbation favors the formation of rings. Also, we found the expected result that the thin disk models generated by the Chazy-Curzon and Zipoy-Voorhees metric with only azimuthal pressure are not stable under a general first order perturbation.

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“…That is, since NEC is violated a different choice of frame may account a negative energy density. Motivation for such a study originates from the consideration of Zipoy-Voorhees metrics which surpasses spherical symmetry with a quadrupole moment by employing a distortion parameter [28][29][30]. In brief, this amounts to a e-mail: habib.mazhari@emu.edu.tr b e-mail: mustafa.halilsoy@emu.edu.tr compress a sphere into an ellipsoidal form through a distortion mechanism.…”

Section: Introductionmentioning

confidence: 99%

$$3+1$$ 3 + 1 -dimensional thin shell wormhole with deformed throat can be supported by normal matter

Mazharimousavi

Halilsoy

2015

Eur. Phys. J. C

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From the physics standpoint the exotic matter problem is a major difficulty in thin shell wormholes (TSWs) with spherical/cylindrical throat topologies. We aim to circumvent this handicap by considering angle dependent throats in 3 + 1 dimensions. By considering the throat of the TSW to be deformed spherical, i.e., a function of θ and ϕ, we present general conditions which are to be satisfied by the shape of the throat in order to have the wormhole supported by matter with positive density in the static reference frame. We provide particular solutions/examples to the constraint conditions.

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Static Axially Symmetric Gravitational Fields

Cited by 253 publications

References 5 publications

Weyl metrics and wormholes

Weyl metrics and wormholes

Stability of general relativistic geometric thin disks

$$3+1$$ 3 + 1 -dimensional thin shell wormhole with deformed throat can be supported by normal matter

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