Axially symmetric static sources of gravitational field

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

doi:10.1088/0264-9381/33/23/235005

Cited by 30 publications

(69 citation statements)

References 47 publications

(116 reference statements)

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“…This fact in turn is related to the well known result that the only regular static and asymptotically flat vacuum spacetime possessing a regular horizon is the Schwarzchild solution [13], while all the others Weyl exterior solutions [14]- [16] exhibit singularities in the curvature invariants (as the boundary of the source approaches the horizon). Sources of different Weyl spacetimes have already been considered by several authors in the past (see for example [17]- [27] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Complexity factors for axially symmetric static sources

2019

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A previously found definition of complexity for spherically symmetric fluid distributions [1], is extended to axially symmetric static sources. In this case there are three different complexity factors, defined in terms of three structure scalars obtained from the orthogonal splitting of the Riemann tensor. All these three factors vanish, for what we consider the simplest fluid distribution, i.e a fluid spheroid with isotropic pressure and homogeneous energy density. However, as in the spherically symmetric case, they can also vanish for a variety of configurations, provided the energy density inhomogeneity terms cancel the pressure anisotropic ones in the expressions for the complexity factors. Some exact analytical solutions of this type are found and analyzed. At the light of the obtained results, some conclusions about the correlation (the lack of it) between symmetry and complexity, are put forward.

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Section: Introductionmentioning

confidence: 99%

Complexity factors for axially symmetric static sources

2019

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“…The spheroidal parameter which appears in the gravitational potential measures the deviation from spherical symmetry. Work on rotating stars utilise an axis-symmetric metric to describe the stellar interior [11,12]. Recently there has been a surge in obtaining exact solutions of the Einstein field equations via embedding [13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

A family of charged compact objects with anisotropic pressure

Maurya

Govender

2017

Eur. Phys. J. C

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Utilizing an ansatz developed by Maurya et al. we present a class of exact solutions of the Einstein-Maxwell field equations describing a spherically symmetric compact object. A detailed physical analysis of these solutions in terms of stability, compactness and regularity indicates that these solutions may be used to model strange star candidates. In particular, we model the strange star candidate Her X-1 and show that our solution conforms to observational data to an excellent degree of accuracy. An interesting and novel phenomenon which arises in this model is the fact that the relative difference between the electromagnetic force and the force due to the pressure anisotropy changing sign within the stellar interior. This may be an additional mechanism required for stability against cracking of the stellar object.

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“…It is to say, the process of solving starts in the interior field equations compatibles with different matter distributions and/or any symmetry considerations and culminates with the suitable exterior Weyl metric matching appropriately at the boundary of the object. This dynamic of work was recently reversed in [13,14] where authors calculate interior metrics successfully matching with either any of the Weyl family vacuum solutions or stationary axially solutions (in particular the Kerr solution). The relevance of this result becomes highlighted in view especially of the fact that the interior line element is constructed in terms of the exterior metric functions evaluated at the boundary, in such a way that both the metric and the energy-momentum tensor are related with the gravitational field.…”

Section: Introductionmentioning

confidence: 99%

Connecting the exterior gravitational field with the energy–momentum tensor of axially symmetric compact objects

Hernández‐Pastora

2020

Eur. Phys. J. C

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A method to construct interior axially symmetric metrics that appropriately match with any vacuum solution of the Weyl family is developed in Hernández-Pastora et al. (Class Quantum Gravity 33:235005, 2016). It was shown, for the case of some vacuum solutions, that the simplest solution for the interior metric leads to sources with wellbehaved energy conditions. Now, we integrate the field equations to obtain the interior metric functions in terms of the anisotropies and pressures of the source. As well, the compatible equations of state for these global models are calculated. The interior metric and the suitable energy-momentum tensor describing the source are constructed in terms of the exterior metric functions. At the boundary of the compact object, the behaviour of a pressure T m , defined from the energymomentum tensor, is shown to be related with the exterior gravitational field. This fact allows us to explore the differences arising at the matter distribution when the spherical symmetry of the global metric is dropped. Finally, an equation derived from the matching conditions is obtained which allows us to calculate the Weyl coefficients of the exterior metric as source integrals. Hence the Relativistic Multipole Moments of the global model can be expressed in terms of the matter distribution of the source.

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Axially symmetric static sources of gravitational field

Cited by 30 publications

References 47 publications

Complexity factors for axially symmetric static sources

Complexity factors for axially symmetric static sources

A family of charged compact objects with anisotropic pressure

Connecting the exterior gravitational field with the energy–momentum tensor of axially symmetric compact objects

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