Orthogonal decomposition of axi-symmetric stationary spacetimes

Kundt, Wolfgang; Trümper, Manfred

doi:10.1007/bf01325677

Cited by 107 publications

(87 citation statements)

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“…Any vector µ is said to be toroidal if it belongs to this plane, poloidal if it is perpendicular (Carter 1970(Carter , 1973. For those particular forms of the matter-energy distribution, such that the energymomentum tensor T µν satisfies the relations (Kundt & Trümper 1966;Carter 1969)…”

Section: Metricmentioning

confidence: 99%

General relativistic models for rotating magnetized neutron stars in conformally flat space–time

Pili

Bucciantini

Zanna

2017

Monthly Notices of the Royal Astronomical Society

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The extraordinary energetic activity of magnetars is usually explained in terms of dissipation of a huge internal magnetic field of the order of 10 15−16 G. How such a strong magnetic field can originate during the formation of a neutron star is still subject of active research. An important role can be played by fast rotation: if magnetars are born as millisecond rotators dynamo mechanisms may efficiently amplify the magnetic field inherited from the progenitor star during the collapse. In this case, the combination of rapid rotation and strong magnetic field determine the right physical condition not only for the development of a powerful jet driven explosion, manifesting as a gamma ray burst, but also for a copious gravitational waves emission. Strong magnetic fields are indeed able to induce substantial quadrupolar deformations in the star. In this paper we analyze the joint effect of rotation and magnetization on the structure of a polytropic and axisymmetric neutron star, within the ideal magnetohydrodynamic regime. We will consider either purely toroidal or purely poloidal magnetic field geometries. Through the sampling of a large parameter space, we generalize previous results in literature, inferring new quantitative relations that allow for a parametrization of the induced deformation, that takes into account also the effects due to the stellar compactness and the current distribution. Finally, in the case of purely poloidal field, we also discuss how different prescription on the surface charge distribution (a gauge freedom) modify the properties of the surrounding electrosphere and its physical implications.

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Section: Metricmentioning

confidence: 99%

General relativistic models for rotating magnetized neutron stars in conformally flat space–time

Pili

Bucciantini

Zanna

2017

Monthly Notices of the Royal Astronomical Society

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“…For spacetimes with two commuting Killing fields, it was first proved by Papapetrou [17] in vacuum and by Kundt and Trümper [13] for fluids that orthogonal transitivity holds. Recall that orthogonal transitivity is the condition that the distribution of 2-surface elements perpendicular to the generators of the symmetry group is surface-forming.…”

Section: Outline Of the Papermentioning

confidence: 99%

Rotating elastic bodies in Einstein gravity

Andersson

Beig

Schmidt

2009

Comm Pure Appl Math

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“…5 We may then choose the two remaining coordinates (x 2 , x 3 ) in one of these 2-surfaces and carry them to the whole spacetime along the integral curves of ξ and η; accordingly, the metric can be written in the form…”

Section: B Form Of the Metricmentioning

confidence: 99%

Bounds on the dragging rate of slowly and differentially rotating relativistic stars

Pareja

2004

Journal of Mathematical Physics

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Bounds on the dragging rate and on the rotational mass-energy in slowly and differentially rotating relativistic stars For relativistic stars rotating slowly and differentially with a positive angular velocity, some properties in relation to the positiveness of the rate of rotational dragging and of the angular momentum density are derived. Also, a new proof for the bounds on the rotational mass-energy is given.

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Orthogonal decomposition of axi-symmetric stationary spacetimes

Abstract: We show that for a wide class of field equations the orbits of the isometry group defining axial symmetry and stationarity admit orthogonal 2-surfaces, The field equations covered by this result include those of a perfect fluid.

Cited by 107 publications

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General relativistic models for rotating magnetized neutron stars in conformally flat space–time

General relativistic models for rotating magnetized neutron stars in conformally flat space–time

Rotating elastic bodies in Einstein gravity

Bounds on the dragging rate of slowly and differentially rotating relativistic stars

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