New static axisymmetric solution of the Einstein field equations

Hernández‐Pastora, J. L.; Martín, Jesús Izquierdo

doi:10.1088/0264-9381/10/12/017

Cited by 23 publications

(43 citation statements)

References 8 publications

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“…In fact, the general term of the series corresponding to the gravitational Dipole and the solutions with Monopole plus any other 2 N -pole moment are written specifically. In Appendix A, the RMM of the general static and axisymmetric solution (6) are written in terms of the coefficients a n , as well as the inverse relation for a solution with arbitrary RMM up to order 9. The method described in [12] can be used to obtain the general term of the series (6) with any finite set of RMM.…”

Section: Calculation Of Msa Coordinates For Any Multipole Solutionmentioning

confidence: 99%

On the calculation and interpretation of MSA coordinates

Hernández‐Pastora¹

2010

Class. Quantum Grav.

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The static solutions of the axially symmetric vacuum Einstein equations with a finite number of Relativistic Multipole Moments (RMM) are described by means of a function that can be written in the same analytic form as the Newtonian gravitational multipole potential. A family of so-called MSA (Multipole-Symmetry Adapted) coordinates are introduced to perform the transformation of the Weyl solutions; a procedure for their calculation at any multipole order is given, and the results for a low order are shown.In analogy with a previous result [10] obtained in Newtonian gravity, the existence of a symmetry of a certain system of differential equations leading to the determination of that kind of multipole solutions in General Relativity is explored. The relationship between the existence of this kind of coordinates and the symmetries mentioned is proved for some cases, and the characterization of the MSA system of coordinates by means of this relationship is discussed.

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Section: Calculation Of Msa Coordinates For Any Multipole Solutionmentioning

confidence: 99%

On the calculation and interpretation of MSA coordinates

Hernández‐Pastora¹

2010

Class. Quantum Grav.

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“…Thus, the explicit solution up to first order, describing a quadrupolar correction to the monopole, is ( note a misprint in the equation (13) in [23])…”

Section: The Monopole-quadrupole Solution M − Qmentioning

confidence: 99%

Geodesics in a Quash-Spherical Spacetime: A Case of Gravitational Repulsion

Herrera

2005

Found Phys Lett

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Geodesics are studied in one of the Weyl metrics, referred to as the M-Q solution. First, arguments are provided, supporting our belief that this space-time is the more suitable (among the known solutions of the Weyl family) for discussing the properties of strong quasi-spherical gravitational fields. Then, the behaviour of geodesics is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical symmetry. Particular attention deserves the change of sign in proper radial acceleration of test particles moving radially along symmetry axis, close to the r = 2M surface, and related to the quadrupole moment of the source.2

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“…Therefore, it should be the M Q (1) solution [5], [6] constructed with this claim. In order to verify this conjecture, it is necessary to check that the metric function Ψ corresponding to the M Q (1) solution generates the Ernst potential (50) up to order q.…”

Section: Analysis Of the Solutionmentioning

confidence: 99%

Approximate gravitational field of a rotating deformed mass

Hernández‐Pastora

2006

Gen Relativ Gravit

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A new approximate solution of vacuum and stationary Einstein field equations is obtained. This solution is constructed by means of a power series expansion of the Ernst potential in terms of two independent and dimensionless parameters representing the quadrupole and the angular momentum respectively. The main feature of the solution is a suitable description of small deviations from spherical symmetry through perturbations of the static configuration and the massive multipole structure by using those parameters. This quality of the solution might eventually provide relevant differences with respect to the description provided by the Kerr solution.

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New static axisymmetric solution of the Einstein field equations

Cited by 23 publications

References 8 publications

On the calculation and interpretation of MSA coordinates

On the calculation and interpretation of MSA coordinates

Geodesics in a Quash-Spherical Spacetime: A Case of Gravitational Repulsion

Approximate gravitational field of a rotating deformed mass

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