Optical Space of the Reissner-Nordström Solutions

We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by exact solutions of Einstein's field equations. A family of these solutions had already be found (de Felice et al., 1995) but here we generalize that result to cases with different charge distribution within the spheres and show, in an appropriate parameter space, that the set of such physically reasonable solutions has a non zero measure. We also perform a perturbation analysis and identify the solutions which are stable against adiabatic radial perturbations. We then suggest that the stable configurations can be considered as classic models of charged particles. Finally our results are used to show that a conjecture of Kristiansson et al. (1998) is incorrect.

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“…Now we see that the set of equations (3), (8) and (9) is complete. The boundary of the physical configuration is identified by the conditions:…”

Section: Existence Of Regular Quasi-critical Spheresmentioning

confidence: 90%

“…We then suggest that the stable configurations can be considered as classic models of charged particles. Finally our results are used to show that a conjecture of Kristiansson et al (1998) is incorrect. …”

mentioning

confidence: 99%

Relativistic charged spheres: II. Regularity and stability

Felice

Siming

1999

Class. Quantum Grav.

105

111

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“…The presence of the factor (r − 3M) in a (c) r can be understood intuitively [17] considering an embedding diagram [18] of the section θ = π/2 of the optical space (S,h ab ), where S is any t = const hypersurface of the Schwarzschild spacetime, and the metrich ab has the coordinate representation [15] …”

Section: Optical Geometrymentioning

confidence: 99%

“…r is the distance from the axis [18] -also called "radius of gyration" [26] because v = (1 − 2M/r) −1/2 Ωr = Ωρ. The centripetal acceleration in the optical space is given by the tangential component of a E , namely…”

Section: Appendix: Centripetal Acceleration In Optical Geometrymentioning

confidence: 99%

Optical geometry analysis of the electromagnetic self-force

Sonego

Abramowicz

2006

Journal of Mathematical Physics

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“…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%

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 Space of the Reissner-Nordström Solutions

Cited by 26 publications

References 13 publications

Relativistic charged spheres: II. Regularity and stability

Relativistic charged spheres: II. Regularity and stability

Optical geometry analysis of the electromagnetic self-force

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

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