The interpretation of some spheroidal metrics

Bonnor, W. B.; Sackfield, A.

doi:10.1007/bf01646273

Cited by 70 publications

(85 citation statements)

References 4 publications

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“…We can also see that the constraint (17) leads to U ± = 0, so this is a "true static disk", in the sense that we can not obtain a counter-rotating interpretation for it. This case corresponds to the Bonnor and Sackfield disk of reference [1]. For the second, simple, case we take µ = k > 0, so that p r = p ϕ = 2α(α − k) and…”

Section: A Family Of Disks With Some Stable Crmmentioning

confidence: 99%

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Relativistic static thin disks: The counterrotating model

Espitia

González

2003

Phys. Rev. D

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A detailed study of the Counter-Rotating Model (CRM) for generic finite static axially symmetric thin disks with nonzero radial pressure is presented. We find a general constraint over the counter-rotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counter-rotating perfect fluids. We also found expressions for the energy density and pressure of the counter-rotating fluids. Then we shown that, in general, there is not possible to take the two counter-rotating fluids as circulating along geodesics neither take the two counter-rotating tangential velocities as equal and opposite. An specific example is studied where we obtain some CRM with well defined counter-rotating tangential velocities and stable against radial perturbations. The CRM obtained are in agree with the strong energy condition, but there are regions of the disks with negative energy density, in violation of the weak energy condition.

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Section: A Family Of Disks With Some Stable Crmmentioning

confidence: 99%

“…These were first studied by Bonnor and Sackfield [1], obtaining pressureless static disks, and by Morgan and Morgan, obtaining static disks with and without radial pressure [2,3]. In connection with gravitational collapse, disks were first studied by Chamorro, Gregory and Stewart [4].…”

Section: Introductionmentioning

confidence: 99%

Relativistic static thin disks: The counterrotating model

Espitia

González

2003

Phys. Rev. D

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“…Exact solutions that have relativistic static thin disks as their sources were first studied by Bonnor and Sackfield [1] and Morgan and Morgan [2,3]. Subsequently, several classes of exact solutions corresponding to static [4][5][6][7][8][9][10][11][12][13] and stationary [14][15][16][17][18] thin disks have been obtained by different authors.…”

Section: Introductionmentioning

confidence: 99%

Conformastatic disk-haloes in Einstein-Maxwell gravity

2013

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We present a relativistic model describing a thin disk surrounded by a halo in presence of an electromagnetic field. The model is obtained by solving the Einstein-Maxwell equations on a particular conformastatic spacetime background and by using the distributional approach for the energymomentum tensor. A class of solutions is obtained in which the gravitational and electromagnetic potentials are completely determined by a harmonic function only. A particular solution is given that is asymptotically flat and singularity-free, and satisfies all the energy conditions.

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“…These were first studied by Bonnor and Sackfield [2], obtaining pressureless static disks, and then by Morgan and Morgan, obtaining static disks with and without radial pressure [3,4]. In connection with gravitational collapse, disks were first studied by Chamorro, Gregory, and Stewart.…”

Section: Introductionmentioning

confidence: 99%

Rotating and counterrotating relativistic thin disks as sources of stationary electrovacuum spacetimes

García-Reyes¹,

González²

2007

Braz. J. Phys.

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A detailed study is presented of the counterrotating model (CRM) for electrovacuum stationary axially symmetric relativistic thin disks of infinite extension without radial stress, in the case when the eigenvalues of the energy-momentum tensor of the disk are real quantities, so that there is not heat flow. We find a general constraint over the counterrotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counterrotating charged dust fluids. We then show that, in some cases, this constraint can be satisfied if we take the two counterrotating tangential velocities as equal and opposite or by taking the two counterrotating streams as circulating along electro-geodesics. However, we show that, in general, it is not possible to take the two counterrotating fluids as circulating along electro-geodesics nor take the two counterrotating tangential velocities as equal and opposite. A simple family of models of counterrotating charged disks based on the Kerr-Newman solution are considered where we obtain some disks with a CRM well behaved. We also show that the disks constructed from the Kerr-Newman solution can be interpreted, for all the values of parameters, as a matter distribution with currents and purely azimuthal pressure without heat flow. The models are constructed using the well-known "displace, cut and reflect" method extended to solutions of vacuum Einstein-Maxwell equations. We obtain, in all the cases, counterrotating Kerr-Newman disks that are in agreement with all the energy conditions.

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The interpretation of some spheroidal metrics

Abstract: ZIPOY recently studied some static gravitational fields in spheroidal coordinates, and endowed them with unfamiliar topologies. We examine three of these fields and show" that they can also be interpreted as fields in space of Euclidean topology.

Cited by 70 publications

References 4 publications

Relativistic static thin disks: The counterrotating model

Relativistic static thin disks: The counterrotating model

Conformastatic disk-haloes in Einstein-Maxwell gravity

Rotating and counterrotating relativistic thin disks as sources of stationary electrovacuum spacetimes

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