Interior solution for the Kerr metric

Hernández‐Pastora, J. L.; Herrera, L.

doi:10.1103/physrevd.95.024003

Cited by 26 publications

(51 citation statements)

References 38 publications

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“…In our frame, it is associated to the basis V a and W a and thus it is related, thanks to the axisymmetry of our background metric (1), to transfer heat along the rotation axis. This effect is also present in the interior Kerr solution found in [27,28]. Concerning the viscosity parameter H, as well known, it is not simple to treat [31] and it is expected to depict peculiar dissipative properties of the fluid.…”

Section: General Case With Vanishing Viscositymentioning

confidence: 84%

An algorithm to generate anisotropic rotating fluids with vanishing viscosity

Viaggiu

2018

Eur. Phys. J. Plus

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Section: General Case With Vanishing Viscositymentioning

confidence: 84%

An algorithm to generate anisotropic rotating fluids with vanishing viscosity

Viaggiu

2018

Eur. Phys. J. Plus

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“…The interior solution for the Kerr metric is still unknown despite of numerous attempts to find it out [47,82,91,97,98]. Recently, a certain progress has been made by Hernandez-Pastora and Herrera [93] who used a model of a viscous, anisotropic distribution of mass density inside rotating body. The post-Newtonian approximation of the Kerr metric (217) in the ellipsoidal coordinates is…”

Section: B Post-newtonian Approximation Of the Kerr Metricmentioning

confidence: 99%

Normal gravity field in relativistic geodesy

2018

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Modern geodesy is subject to a dramatic change from the Newtonian paradigm to Einstein's theory of general relativity. This is motivated by the ongoing advance in development of quantum sensors for applications in geodesy including quantum gravimeters and gradientometers, atomic clocks and fiber optics for making ultra-precise measurements of the geoid and multipolar structure of the Earth's gravitational field. At the same time, Very Long Baseline Interferometry, Satellite Laser Ranging and Global Navigation Satellite System have achieved an unprecedented level of accuracy in measuring 3-d coordinates of the reference points of the International Terrestrial Reference Frame and the world height system. The main geodetic reference standard to which gravimetric measurements of the of Earth's gravitational field are referred, is a normal gravity field represented in the Newtonian gravity by the field of a uniformly rotating, homogeneous Maclaurin ellipsoid which mass and quadrupole momentum are equal to the total mass and (tide-free) quadrupole moment of the Earth gravitational field. The present paper extends the concept of the normal gravity field from the Newtonian theory to the realm of general relativity. We focus our attention on the calculation of the post-Newtonian approximation of the normal field that is sufficient for current and near-future practical applications. We show that in general relativity the level surface of homogeneous and uniformly rotating fluid is no longer described by the Maclaurin ellipsoid in the most general case but represents an axisymmetric spheroid of the fourth order with respect to the geodetic Cartesian coordinates. At the same time, admitting a post-Newtonian inhomogeneity of the mass density in the form of concentric elliptical shells allows to preserve the level surface of the fluid as an exact ellipsoid of rotation. We parametrize the mass density distribution and the level surface with two parameters which are intrinsically connected to the existence of the residual gauge freedom, and derive the post-Newtonian normal gravity field of the rotating spheroid both inside and outside of the rotating fluid body. The normal gravity field is given, similarly to the Newtonian gravity, in a closed form by a finite number of the ellipsoidal harmonics. We employ transformation from the ellipsoidal to spherical coordinates to deduce a more conventional post-Newtonian multipolar expansion of scalar and vector gravitational potentials of the rotating spheroid. We compare these expansions with that of the normal gravity field generated by the Kerr metric and demonstrate that the Kerr metric has a fairly limited application in relativistic geodesy as it does not match the normal gravity field of the Maclaurin ellipsoid already in the Newtonian limit. We derive the post-Newtonian generalization of the Somigliana formula for the normal gravity field measured on the surface of the rotating spheroid and employed in practical work for measuring the Earth gravitational field anomalies. Finally, ...

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“…We refer the reader to [1] for the details and some intermediate calculations. At this point we would like to call attention to two misprints in [1], that have been corrected here, namely: the equation (11) below, is the right version of the corresponding equation (36) appearing in [1]. Also, a misprint appearing in the equation (40) in [1], has been corrected in the last of the forthcoming equations (26).…”

Section: A Source For the Exterior Kerr Solutionmentioning

confidence: 99%

“…At this point we would like to call attention to two misprints in [1], that have been corrected here, namely: the equation (11) below, is the right version of the corresponding equation (36) appearing in [1]. Also, a misprint appearing in the equation (40) in [1], has been corrected in the last of the forthcoming equations (26). It is worth emphasizing, however, that such misprints are irrelevant for the discussion presented in [1], since all the calculations in that reference were carried out using the right expressions, written down here.…”

Section: A Source For the Exterior Kerr Solutionmentioning

confidence: 99%

“…In a recent paper [1], we have proposed an interior solution for the Kerr metric [2], satisfying the matching conditions on the boundary surface of the matter distribution, and endowed with reasonable physical properties, at least for a range of values of the parameters, which includes values considered in the existing literature to describe realistic models of rotating neutron stars and white dwarfs.…”

Section: Introductionmentioning

confidence: 99%

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Physical properties of a source of the Kerr metric: Bound on the surface gravitational potential and conditions for the fragmentation

Herrera

Hernández‐Pastora

2017

Phys. Rev. D

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We investigate some important physical aspects of a recently presented interior solution for the Kerr metric. It is shown that, as in the spherically symmetric case, there is a specific limit for the maximal value of the surface potential (degree of compactness), beyond which, unacceptable physical anomalies appear. Such a bound is related to the appearance of negative (repulsive) gravitational acceleration, that is accompanied by the appearance of negative values of the pressure. A detailed discussion on this effect is presented. We also study the possibility of a fragmentation scenario, assuming that the source leaves the equilibrium, and we bring out the differences with the spherically symmetric case.

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Interior solution for the Kerr metric

Cited by 26 publications

References 38 publications

An algorithm to generate anisotropic rotating fluids with vanishing viscosity

An algorithm to generate anisotropic rotating fluids with vanishing viscosity

Normal gravity field in relativistic geodesy

Physical properties of a source of the Kerr metric: Bound on the surface gravitational potential and conditions for the fragmentation

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