On the calculation and interpretation of MSA coordinates

Hernández‐Pastora, J. L.

doi:10.1088/0264-9381/27/4/045006

Cited by 12 publications

(50 citation statements)

References 22 publications

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“…We shall back to the explicit expression forr 1 later, but previously let us redefine the problem to solve enunciated at Statement 1. In accordance with the discussion in [1] we have showed that conditions (i)-(ii) lead to the same equations that the pair of conditions (i)-(iii), and therefore the problem we want to solve is now formulated as follows: Statement 2 Letr =r(x, y),ŷ =ŷ(x, y) be a pair of surfaces with the relationship given by the expression (15). Then, the radial coordinate of the MSA system of coordinates {r,ŷ} with which the MQ-solution is described by the metric function g M Q 00 = −1 + 2M r + 2QP 2 (ŷ) r 3 , is given by the solution of the differential equation (16) with the boundary conditionr(x, y = ±1) =r 1 and asymptotic conditionsr(R → ∞) = R + α,ŷ(R → ∞) = ω.…”

Section: Resolution Strategiessupporting

confidence: 90%

“…In [1], a coordinate transformation with a good asymptotic Cartesian behaviour was performed as followŝ…”

Section: Resolution Strategiesmentioning

confidence: 99%

“…The possibility of extrapolating the symmetries obtained in NG [7] to GR, as well as characterizing the solutions with a finite number of RMM by means of group-invariant solutions, are the relevant features of a proposed system of coordinates. In [1] an answer to these questions was sought by introducing a family of coordinate systems referred to as MSA (Multipole-Symmetry Adapted). The MSA system of coordinates [1] were introduced to generalize the ER coordinates with the aim of inheriting its benefits in describing the solution with a finite number of RMM analogously to the Schwarzschild case.…”

Section: Introductionmentioning

confidence: 99%

“…In [1] an answer to these questions was sought by introducing a family of coordinate systems referred to as MSA (Multipole-Symmetry Adapted). The MSA system of coordinates [1] were introduced to generalize the ER coordinates with the aim of inheriting its benefits in describing the solution with a finite number of RMM analogously to the Schwarzschild case.…”

Section: Introductionmentioning

confidence: 99%

“…where ∇, △ denote the gradient and Laplacian operators respectively with respect to an Euclidean metric (see [1] for details), and…”

mentioning

confidence: 99%

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A quadrupolar generalization of the Erez-Rosen coordinates

Hernández‐Pastora¹

2019

Class. Quantum Grav.

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The MSA system of coordinates [1] for the M Q-solution [2] is proved to be the unique solution of certain partial differential equation with boundary and asymptotic conditions. Such a differential equation is derived from the orthogonality condition between two surfaces which hold a functional relationship.The obtained expressions for the MSA system recover the asymptotic expansions previously calculated [1] for those coordinates, as well as the Erez-Rosen coordinates in the spherical case. It is also shown that the event horizon of the M Q-solution can be easily obtained from those coordinates leading to already known results. But in addition, it allows us to correct a mistaken conclusion related to some bound imposed to the value of the quadrupole moment [3].Finally, it is explored the possibility of extending this method of generalizing the Erez-Rosen coordinates to the general case of solutions with any finite number of Relativistic Multipole Moments (RMM). It is discussed as well, the possibility of determining the * E.T.S. Ingeniería Industrial de Béjar. Phone: +34 923 408080 Ext 2223. Also at +34 923 294400 Ext 1574. e-mail address: jlhp@usal.es Weyl moments of those solutions from their corresponding MSA coordinates, aiming to establish a relation between the uniqueness of the MSA coordinates and the solutions itself.1 The general solution of the static vacuum Einstein equations for the axisymmetric case depends on only two metric functions namely Ψ, γ, and in addition, γ is obtained from Ψ by means of a quadrature. Therefore, a solution of these equations is characterized by that metric function Ψ = 1 2 ln(−g 00 ).

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Section: Resolution Strategiessupporting

confidence: 90%

“…In [1], a coordinate transformation with a good asymptotic Cartesian behaviour was performed as followŝ…”

Section: Resolution Strategiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…where ∇, △ denote the gradient and Laplacian operators respectively with respect to an Euclidean metric (see [1] for details), and…”

mentioning

confidence: 99%

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A quadrupolar generalization of the Erez-Rosen coordinates

Hernández‐Pastora¹

2019

Class. Quantum Grav.

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Exact Solutions—Field Moments

Söffel¹,

Han

2019

Astronomy and Astrophysics Library

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On the usefulness of relativistic space-times for the description of the Earth’s gravitational field

Söffel

Frutos

2016

J Geod

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The usefulness of relativistic space-times for the description of the Earth's gravitational field is investigated. A variety of exact vacuum solutions of Einstein's field equations (Schwarzschild, Erez and Rosen, Gutsunayev and Manko, Hernández-Pastora and Martín, Kerr, Quevedo, and Mashhoon) are investigated in that respect. It is argued that because of their multipole structure and influences from external bodies, all these exact solutions are not really useful for the central problem. Then, approximate space-times resulting from an MPM or post-Newtonian approximation are considered. Only in the DSX formalism that is of the first post-Newtonian order, all aspects of the problem can be tackled: a relativistic description (a) of the Earth's gravity field in a well-defined geocentric reference system (GCRS), (b) of the motion of solar system bodies in a barycentric reference system (BCRS), and (c) of inertial and tidal terms in the geocentric metric describing the external gravitational field. A relativistic SLR theory is also discussed with respect to our central problem. Orders of magnitude of many effects related to the Earth's gravitational field and SLR are given. It is argued that a formalism with accuracies better than of the first post-Newtonian order is not yet available.

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On the calculation and interpretation of MSA coordinates

Cited by 12 publications

References 22 publications

A quadrupolar generalization of the Erez-Rosen coordinates

A quadrupolar generalization of the Erez-Rosen coordinates

Exact Solutions—Field Moments

On the usefulness of relativistic space-times for the description of the Earth’s gravitational field

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