Optical reference geometry of Kerr-Newman spacetimes

Stuchlík, Zdeněk; Hledík, Stanislav; Juran, Josef

doi:10.1088/0264-9381/17/14/307

Cited by 22 publications

(49 citation statements)

References 15 publications

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“…(The relation of photon circles to centrifugal-plus-Coriolis force in the limit v → 1 is also discussed by Stuchlik, Hledik and Jurán [23]; note, however, that their work is restricted to the equatorial plane of the Kerr-Newman spacetime throughout. )…”

Section: Centrifugal and Coriolis Force In The Kerr-newman Spacementioning

confidence: 88%

A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole

Haße

Perlick

2006

Journal of Mathematical Physics

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Consider, in the domain of outer communication M+ of a Kerr-Newman black hole, a point p (observation event) and a timelike curve γ (worldline of light source). Assume that γ (i) has no past end-point, (ii) does not intersect the caustic of the past light-cone of p, and (iii) goes neither to the horizon nor to infinity in the past. We prove that then for infinitely many positive integers k there is a past-pointing lightlike geodesic λ k of (Morse) index k from p to γ, hence an observer at p sees infinitely many images of γ. Moreover, we demonstrate that all lightlike geodesics from an event to a timelike curve in M+ are confined to a certain spherical shell. Our characterization of this spherical shell shows that in the Kerr-Newman spacetime the occurrence of infinitely many images is intimately related to the occurrence of centrifugal-plus-Coriolis force reversal.

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Section: Centrifugal and Coriolis Force In The Kerr-newman Spacementioning

confidence: 88%

A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole

Haße

Perlick

2006

Journal of Mathematical Physics

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“…By simultaneously solving the coupled equations, the structure of the polytrope is obtained; it is characterized by the profiles of the energy density, pressure, mass, and two metric coefficients (g tt , g rr ) giving the geometry of the internal spacetime of the polytropic sphere. The spacetime structure can be reflected by the embedding diagrams of the ordinary space and the optical reference geometry reflecting some hidden properties of the spacetime [125,126]. The other relevant characteristics of the polytropes are the gravitational potential energy and the binding energy [118].…”

Section: Introductionmentioning

confidence: 99%

General relativistic polytropes with a repulsive cosmological constant

2016

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Spherically symmetric equilibrium configurations of perfect fluid obeying a polytropic equation of state are studied in spacetimes with a repulsive cosmological constant. The configurations are specified in terms of three parameters-the polytropic index n, the ratio of central pressure and central energy density of matter σ, and the ratio of energy density of vacuum and central density of matter λ. The static equilibrium configurations are determined by two coupled first-order nonlinear differential equations that are solved by numerical methods with the exception of polytropes with n = 0 corresponding to the configurations with uniform distribution of energy density, when the solution is given in terms of elementary functions. The geometry of the polytropes is conveniently represented by embedding diagrams of both the ordinary space geometry and the optical reference geometry reflecting some dynamical properties of the geodesic motion. The polytropes are represented by radial profiles of energy density, pressure, mass, and metric coefficients. For all tested values of n > 0, the static equilibrium configurations with fixed parameters n, σ, are allowed only up to a critical value of the cosmological parameter λc = λc(n, σ). In the case of n > 3, the critical value λc tends to zero for special values of σ. The gravitational potential energy and the binding energy of the polytropes are determined and studied by numerical methods. We discuss in detail the polytropes with extension comparable to those of the dark matter halos related to galaxies, i.e., with extension ℓ > 100 kpc and mass M > 10 12 M⊙. For such largely extended polytropes the cosmological parameter relating the vacuum energy to the central density has to be larger than λ = ρvac/ρc ∼ 10 −9 . We demonstrate that extension of the static general relativistic polytropic configurations cannot exceed the so called static radius related to their external spacetime, supporting the idea that the static radius represents a natural limit on extension of gravitationally bound configurations in an expanding universe dominated by the vacuum energy.PACS numbers: 98.80. Es,

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“…We believe the pseudo-Newtonian approach could be useful in modelling self-graviting discs around SdS and KdS blackholes. It should be noticed in this connection that character of the centrifugal force, which is relevant in determining the structure of thick discs, is clearly reflected by the embedding diagrams of the optical geometry (see [14]). …”

Section: Bh Spacetimes Ns Spacetimesmentioning

confidence: 92%

“…Acceleration necessary to keep a particle in an uniform circular motion in the equatorial plane (θ = π/2) can be expressed due to relation (8) in the simple form [5], [14] …”

Section: Equatorial Circular Motionmentioning

confidence: 99%

“…Later, the definition of the optical reference geometry and related inertial forces was generalized, extending its applicability to any spacetime [4], [5], [6], [7]. The optical reference geometry was also thoroughly studied in particular spacetimes, such as Schwarzschild-de Sitter [8], [9], Reissner-Nordström [10], Reissner-Nordström-de Sitter [11], Kerr [12], [13] or Kerr-Newman [14], illustrated by embedding diagrams [15], [16], [17], and the inertial forces formalism was applied for solving specific problems in relativistic dynamics [18], [19]. Behaviour of the centrifugal force is closely related to the shape of embedding diagrams of the optical geometry, therefore many properties of the relativistic dynamics in the spacetimes were effectively illustrated and directly visualized.…”

Section: Introductionmentioning

confidence: 99%

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Optical Reference Geometry and Inertial Forces in Kerr-De Sitter Spacetimes

Kovář¹,

Stuchlík²

2008

The Eleventh Marcel Grossmann Meeting

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Abstract. Optical reference geometry and related concept of inertial forces are investigated in Kerr-de Sitter spacetimes. Properties of the inertial forces are summarized and their typical behaviour is illustrated. The intuitive 'Newtonian' application of the forces in the relativistic dynamics is demonstrated in the case of the test particle circular motion, static equilibrium positions and perfect fluid toroidal configurations. Features of the optical geometry are illustrated by the embedding diagrams of its equatorial plane. The embedding diagrams do not cover whole the stationary regions of the spacetimes, therefore the limits of embeddability are established. A shape of the embedding diagrams is related to the behaviour of the centrifugal force and it is characterized by the number of turning points of the diagrams. Discussion of the number of embeddable photon circular orbits is also included and the typical embedding diagrams are constructed. The Kerr-de Sitter spacetimes are classified according to the properties of the inertial forces and embedding diagrams.

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Optical reference geometry of Kerr-Newman spacetimes

Cited by 22 publications

References 15 publications

A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole

A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole

General relativistic polytropes with a repulsive cosmological constant

Optical Reference Geometry and Inertial Forces in Kerr-De Sitter Spacetimes

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