No abstract

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,

Abstract. Discussion of the equatorial photon motion in Kerr-Newman blackhole and naked-singularity spacetimes with a non-zero cosmological constant is presented. Both repulsive and attractive cosmological constants are considered. An appropriate 'effective potential' governing the photon radial motion is defined, circular photon orbits are determined, and their stability with respect to radial perturbations is established. The spacetimes are divided into separated classes according to the properties of the 'effective potential'. There is a special class of Kerr-Newman-de Sitter black-hole spacetimes with the restricted repulsive barrier. In such spacetimes, photons with high positive and all negative values of their impact parameter can travel freely between the outer black-hole horizon and the cosmological horizon due to an interplay between the rotation of the source and the cosmological repulsion. It is shown that this type of behavior of the photon motion is connected to an unusual relation between the values of the impact parameters of the photons and their directional angles relative to outward radial direction as measured in the locally non-rotating frames. Surprisingly, some photons counterrotating in these frames have positive impact parameter. Such photons can be both escaping or captured in the black-hole spacetimes with the restricted repulsive barrier. For the black-hole spacetimes with a standard, divergent repulsive barrier of the equatorial photon motion, the counterrotating photons with positive impact parameters must all be captured from the region near the black-hole outer horizon as in the case of Kerr black holes, while they all escape from the region near the cosmological horizon. Further, the azimuthal motion is discussed and photon trajectories are given in typical situations. It is shown that for some photons with negative impact parameter turning points of their azimuthal motion can exist.

String theory predicts the existence of extremely compact objects spinning faster than Kerr black holes. The spacetime exterior to such superspinars is described by Kerr naked singularity geometry breaking the black-hole limit on the internal angular momentum. We demonstrate that the conversion of Kerr superspinars into a near-extreme black hole due to an accretion counterrotating Keplerian disc is much more effective in comparison with the case of a corotating one since both the accreted rest mass necessary for conversion and the evolution time of conversion are by orders smaller for counterrotating discs. The conversion time of Kerr superspinars is given for several accretion regimes, and it is shown that the self-regulated accretion flow implies fastest evolution to the black-hole state. In the final stages of the conversion, Kerr superspinars can serve as very efficient particle accelerators in the region where the black-hole horizon forms.