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

Kovář, Jiří; Stuchlík, Zdeněk

doi:10.1142/9789812834300_0339

Cited by 4 publications

(8 citation statements)

References 17 publications

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“…The velocity profiles of the geodetical discs and perfect fluid tori in the locally non-rotating frames were studied in [37,38,39,40,41,42]. Further, the test particle and perfect fluid properties were treated also in the framework of the optical reference geometry [43,44,45] allowing introduction of inertial forces in the intuitive Newtonian way [46]. Motion of photons in the Reissner-Nordström-de Sitter and more general Kerr-Newman-(anti-)de Sitter spacetimes is discussed in the papers [47,48].…”

Section: Introductionmentioning

confidence: 99%

Pseudo-Newtonian and general relativistic barotropic tori in Schwarzschild–de Sitter spacetimes

Stuchlík

Slaný

Kovář

2009

Class. Quantum Grav.

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106

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Pseudo-Newtonian gravitational potential introduced in spherically symmetric black-hole spacetimes with a repulsive cosmological constant is tested for equilibrium toroidal configurations of barotropic perfect fluid orbiting the black holes. Shapes and potential depths are determined for the marginally stable barotropic tori with uniform distribution of specific angular momentum, using both the pseudo-Newtonian and fully relativistic approach. For the adiabatic (isoentropic) perfect fluid, temperature profiles, mass-density and pressure profiles and total masses of pseudo-Newtonian and relativistic tori are compared providing important information on the relevance of the test-disc approximation in both the approaches. It is shown that the pseudo-Newtonian approach can be precise enough and useful for the modelling of accretion discs in the Schwarzschild-de Sitter spacetimes with the cosmological parameter y = ΛM 2 /3 10 −6 . For astrophysically relevant black holes with y < 10 −25 , this statement is tested and shown to be precise in few percent for both accretion and excretion tori and for the marginally bound, i.e., maximally extended tori allowing simultaneous inflow to the black hole and outflow to the outer space.PACS numbers: 95.30.Lz, 98.62.Mw, 98.80.Es

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Section: Introductionmentioning

confidence: 99%

Pseudo-Newtonian and general relativistic barotropic tori in Schwarzschild–de Sitter spacetimes

Stuchlík

Slaný

Kovář

2009

Class. Quantum Grav.

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106

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“…Even if the results presented in Subsec. 4.1 are mostly known from mapping of the test particle motion in conformal hypersurfaces [36,44,45,48,50], they enclose and contextualize the brand-new results introduced in Subsec. 4.2.…”

Section: Introductionmentioning

confidence: 93%

“…in the case of a general motion, as it follows from relations (21) and (55) [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]. Thus, the fluid flow lines in Σ t along which the centrifugal force vanishes independently of velocity are mapped by geodesics inΣ t .…”

Section: Conformal Transformation C = E −φmentioning

confidence: 99%

“…The first force representation benefits from the hypersurface projection of the fluid four-acceleration field, and from its decomposition in the framework of the so-called 'optical reference geometry' that was introduced along with the mapping of test particle motion in the proper conformal hypersurface [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]. This decomposition enables us to introduce the so-called 'inertial forces' that are represented by the velocity and charge independent gravitational force, the velocity dependent and charge independent centrifugal, Coriolis and Euler forces, whereas the sum of these forces vanishes along geodesics -trajectories of free test particles.…”

Section: Introductionmentioning

confidence: 99%

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Charged fluids encircling compact objects: force representations and conformal geometries

Kovář¹,

Kojima²,

Slaný³

et al. 2020

Class. Quantum Grav.

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Charged fluids rotating around compact objects can form unique equilibrium structures when ambient large-scale electromagnetic fields combine with strong gravity. Equatorial as well as off-equatorial toroidal structures are among such figures of equilibrium with a direct relevance for astrophysics. To investigate their geometrical shapes and physical properties in the near-horizon regime, where effects of general relativity play a significant role, we commonly employ a scheme based on the energy-momentum conservation written in a standard representation. Here, we develop its interesting alternatives in terms of two covariant force representations, both based on a hypersurface projection of the energy-momentum conservation. In a proper hypersurface, space-like forces can be defined, following from a decomposition of the fluid four-acceleration. Each of the representations provides us with an insight into properties of the fluid flow, being well reflected in related conformal hypersurface geometries; we find behaviour of centrifugal forces directly related to geodesics of these conformal hypersurfaces and their embedding diagrams. We also reveal correspondence between the charged fluid flow world-lines from an ordinary spacetime, and world-lines determined by a charged test particles equation of motion in a conformal spacetime.

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“…By the use of embedding diagrams of both ordinary geometry and optical reference geometry, Refs. [20] and [21] have shown that in the vicinity of the static radius, the geometry of de Sitter space-time is analogous to an asymptotically flat space-time. Thus, eq.…”

Section: Introductionmentioning

confidence: 99%

Remarks on the black hole shadows in Kerr-de Sitter space times

Omwoyo,

Belich,

Fabris

et al. 2021

Preprint

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This work is geared towards analysis of shadows cast by Kerr-de Sitter (KdS) and Kerr-de Sitter Revisited (RKdS) black holes. Considering observers in the vicinity of the static radius, we derive the impact parameters defining the apparent positions of the shadows. Such observers are of interest to our work because embedding diagrams have shown that de Sitter space-time is analogous to an asymptotically flat one in the vicinity of the static radius. We also perform a comparative analysis between our result with that in Ref. [1]. Furthermore, we numerically obtain the radii of curvature, vertical diameters and horizontal diameters of the shadows. We find that for Λ = 1.11 × 10 −52 m −2 , M87* observations cannot distinguish a RKdS black hole shadow from that of a Kerr black hole. Additionally, for the same value of Λ, KdS and RKdS black hole shadows are identical. Previously, it has also been shown that when Λ = 1.11 × 10 −52 m −2 , KdS and Kerr black hole shadows are indistinguishable. Utilizing the 2017 EHT observations of M87* on the allowed range of the characteristic radius of the shadow, we obtain constraints on both black holes. When, a/M > 0.812311, we observe that large angles of inclination (θ > 30.5107 • ) do not pass the constraints for both KdS and RKdS black holes.

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

Cited by 4 publications

References 17 publications

Pseudo-Newtonian and general relativistic barotropic tori in Schwarzschild–de Sitter spacetimes

Pseudo-Newtonian and general relativistic barotropic tori in Schwarzschild–de Sitter spacetimes

Charged fluids encircling compact objects: force representations and conformal geometries

Remarks on the black hole shadows in Kerr-de Sitter space times

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