New Formulation of the Axially Symmetric Gravitational Field Problem. II

Ernst, Frederick J.

doi:10.1103/physrev.168.1415

Cited by 533 publications

(368 citation statements)

References 3 publications

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“…Although the whole system of equations can be reduced to two complex partial differential equations [1] and special techniques have been developed to generate solutions, for instance the ones reviewed in [2], [3] for vacuum fields, we still lack exact solutions whose physical interpretation is appealing.…”

Section: Introductionmentioning

confidence: 99%

Differential form approach for stationary axisymmetric Maxwell fields in general relativity

Fernández–Jambrina

Chinea

1994

Class. Quantum Grav.

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A formulation for stationary axisymmetric electromagnetic fields in general relativity is derived by casting them into the form of an anisotropic fluid. Several simplifications of the formalism are carried out in order to analyze different features of the fields, such as the derivation of electromagnetic sources for the Maxwell field in the form of thin layers, construction of new solutions, and generation techniques.

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Section: Introductionmentioning

confidence: 99%

Differential form approach for stationary axisymmetric Maxwell fields in general relativity

Fernández–Jambrina

Chinea

1994

Class. Quantum Grav.

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“…Note that we have displaced the origin of the z axis in z 0 . This solution can be generated, in these coordinates, using the well-known complex potential formalism proposed by Ernst [44] from the Kerr vacuum solution [1]. When c = 1 this solution reduces to the Kerr vacuum solution.…”

Section: Disks From a Kerr-newman Solutionmentioning

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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“…Using the above line element, the Einstein-Maxwell equations can be reformulated, via Ernst's procedure [40], in terms of two complex potentials E and Φ as follow:…”

Section: Six-parameter Solutionmentioning

confidence: 99%

Realistic exact solution for the exterior field of a rotating neutron star

2006

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A new six-parametric, axisymmetric and asymptotically flat exact solution of Einstein-Maxwell field equations having reflection symmetry is presented. It has arbitrary physical parameters of mass, angular momentum, mass-quadrupole moment, current octupole moment, electric charge and magnetic dipole, so it can represent the exterior field of a rotating, deformed, magnetized and charged object; some properties of the closed-form analytic solution such as its multipolar structure, electromagnetic fields and singularities are also presented. In the vacuum case, this analytic solution is matched to some numerical interior solutions representing neutron stars, calculated by Berti & Stergioulas [1], imposing that the multipole moments be the same. As an independent test of accuracy of the solution to describe exterior fields of neutron stars, we present an extensive comparison of the radii of innermost stable circular orbits (ISCOs)

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New Formulation of the Axially Symmetric Gravitational Field Problem. II

Cited by 533 publications

References 3 publications

Differential form approach for stationary axisymmetric Maxwell fields in general relativity

Differential form approach for stationary axisymmetric Maxwell fields in general relativity

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

Realistic exact solution for the exterior field of a rotating neutron star

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