Exact self-gravitating disks and rings: A solitonic approach

Letelier, Patrício S.; Oliveira, Samuel Rocha de

doi:10.1063/1.527800

Cited by 67 publications

(71 citation statements)

References 13 publications

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“…The stability of circular geodesics in smooth axially symmetric stress-energy distributions was first considered in [12], in which some remarks about their vertical stability in the limit of an infinitesimally thin disk are presented. During the last decades, many exact solutions representing thin disks were obtained, both in GR (see for example [13][14][15][16][17][18][19][20] and the reviews [4,5]) and in modified theories of gravity [21,22], mainly based * rss.vieira@usp.br † javier@ufscar.br ‡ asaa@ime.unicamp.br on the formalism of distribution-valued curvature tensors proposed by Taub [23]. For razor-thin disks, such an approach is consistent with the results about distributional sources in general relativity obtained by Geroch and Traschen [24], which provide an adequate framework to deal with distribution-valued curvature tensors with support on spacetime hypersurfaces.…”

Section: Introductionmentioning

confidence: 99%

Vertical stability of circular orbits in relativistic razor-thin disks

2016

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During the last few decades, there has been a growing interest in exact solutions of Einstein equations describing razor-thin disks. Despite the progress in the area, the analytical study of geodesic motion crossing the disk plane in these systems is not yet so developed. In the present work, we propose a definite vertical stability criterion for circular equatorial timelike geodesics in static, axially symmetric thin disks, possibly surrounded by other structures preserving axial symmetry. It turns out that the strong energy condition for the disk stress-energy content is sufficient for vertical stability of these orbits. Moreover, adiabatic invariance of the vertical action variable gives us an approximate third integral of motion for oblique orbits which deviate slightly from the equatorial plane. Such new approximate third integral certainly points to a better understanding of the analytical properties of these orbits. The results presented here, derived for static spacetimes, may be a starting point to study the motion around rotating, stationary razor-thin disks. Our results also allow us to conjecture that the strong energy condition should be sufficient to assure transversal stability of periodic orbits for any singular timelike hypersurface, provided it is invariant under the geodesic flow.

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Section: Introductionmentioning

confidence: 99%

Vertical stability of circular orbits in relativistic razor-thin disks

2016

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“…[261,208,209,51,71,72]), none of the latter has yet been specified to the case generated by a concrete realistic body such as ring, disc or torus (cf. the last paragraph of section IV in [190]). …”

Section: Exact Solutionmentioning

confidence: 99%

Towards Gravitating Discs Around Stationary Black Holes

Semerák

2002

Gravitation: Following the Prague Inspiration

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This article outlines the search for an exact general relativistic description of the exterior (vacuum) gravitational field of a rotating spheroidal black hole surrounded by a realistic axially symmetric disc of matter. The problem of multi-body stationary spacetimes is first exposed from the perspective of the relativity theory (section 1) and astrophysics (section 2), listing the basic methods employed and results obtained. Then (in section 3) basic formulas for stationary axisymmetric solutions are summarized. Sections 4 and 5 review what we have learnt with MiroslavŽáček and Tomáš Zellerin about certain static and stationary situations recently. Concluding remarks are given in section 6. Although the survey part is quite general, the list of references cannot be complete. Our main desideratum was the informative value rather than originality -novelties have been preferred, mainly reviews and those with detailed introductions. The fields of multi-body systems involving black holesThe subject of self-gravitating sources around rotating black holes is interesting in several respects, relevant from the point of view of the relativity theory itself as well as in the astrophysical context.First, due to the non-linearity of Einstein's equations, the field of a multi-body system is a traditional challenge where one typically does not manage with a simple superposition. 1 On the first post-Newtonian level, the "celestial mechanics" of gravitationally interacting bodies can be kept linear [89,90], but in the strong-field region the interaction may bring surprising features that have only been described in a very few cases yet (for a two-body problem -today at the centre of attention because of the expected gravitational waves from colliding compact binaries, "the current state of art is the third post-Newtonian approximation" [91]).The second point in which the problem embodies the essence of general relativity is the effect of inertial frame dragging due to the rotation of the sources. Contrary to the Newtonian treatment which does not discriminate between static and stationary situation, the field is now determined not only by mass-energy configuration, but also by its motion within the bodies. The inertial space can be imagined as a viscous fluid mixed by the sources. In today's "gravitoelectromagnetic" language, gravity has not only an electric component, generated by the mass, but also a magnetic one, generated by mass currents; see [245, 103, 215, 298, 147, 79, 202, 201, 1 Even the problem of an "isolated" object is very difficult (mainly if its motion must be found as well, not mentioning the interior field) unless one makes some simple assumptions about its multipole structure; see e.g. [98,99,17] for a treatment of bodies with matter interior, [297] for that also valid for singular bodies such as black holes, and [40] for the case of point-like particles.

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“…Static thin disks without radial pressure were first studied by Bonnor and Sackfield [8], and Morgan and Morgan [9], and with radial pressure also by Morgan and Morgan [10]. Several classes of exact solutions of the Einstein field equations corresponding to static thin disks with or without radial pressure have been obtained by different authors [11][12][13][14][15][16][17]. Rotating thin disks that can be considered as a source of a Kerr metric were presented by Bicák and Ledvinka [18], while rotating disks with heat flow were were studied by González and Letelier [19].…”

Section: Introductionmentioning

confidence: 99%

Models of spherical shells as sources of Majumdar–Papapetrou type spacetimes

García-Reyes

2017

Gen Relativ Gravit

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By starting with a seed Newtonian potential-density pair we construct relativistic thick spherical shell models for a Majumdar-Papapetrou type conformastatic spacetime. As a simple example, we considerer a family of Plummer-Hernquist type relativistic spherical shells. As a second application, these structures are then used to model a system composite by a dust disk and a halo of matter. We study the equatorial circular motion of test particles around such configurations. Also the stability of the orbits is analyzed for radial perturbation using an extension of the Rayleigh criterion. The models considered satisfying all the energy conditions. *

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Exact self-gravitating disks and rings: A solitonic approach

Cited by 67 publications

References 13 publications

Vertical stability of circular orbits in relativistic razor-thin disks

Vertical stability of circular orbits in relativistic razor-thin disks

Towards Gravitating Discs Around Stationary Black Holes

Models of spherical shells as sources of Majumdar–Papapetrou type spacetimes

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