The Schwarzschild-de Sitter space-time describes the gravitational field of a spherically symmetric mass in a universe with cosmological constant Λ. Based on this space-time we calculate Solar system effects like gravitational redshift, light deflection, gravitational time delay, Perihelion shift, geodetic or de Sitter precession, as well as the influence of Λ on a Doppler measurement, used to determine the velocity of the Pioneer 10 and 11 spacecraft. For Λ = Λ0 ∼ 10 −52 m −2 the cosmological constant plays no role for all of these effects, while a value of Λ ∼ −10 −37 m −2 , if hypothetically held responsible for the Pioneer anomaly, is not compatible with the Perihelion shift.
c 1 c 2 c 1 + L ′2 . For nonvanishingñ, E, andL the maximum of the parabola is no longer located at ξ = 0 or, equivalently, the zeros are no longer symmetric with respect to ξ = 0. Only for vanishingñ, E, orL both cones are symmetric with respect to the equatorial plane.The ϑ-motion can be classified according to the sign of c 2 − L ′2 :1. If c 2 − L ′2 < 0 then Θ ξ has 2 positive zeros for L ′ Eñ > 0 and ϑ ∈ (0, π/2), so that the particle moves above the equatorial plane without crossing it. If L ′ Eñ < 0 then ϑ ∈ (π/2, π). TO CEO EO D 0 C B O BO EO ⋆ ⋆ ⋆ EO D 0 CBO ⋆ ⋆ ⋆ ⋆ ⋆ BO EO (b) Taub-NUT space-time II. The CEO (red) starts at the horizon r−, the CBO (blue) starts at the horizon r− and terminates at the horizon r+. FIG. 10: Topology of orbits in Carter-Penrose diagrams of Taub-NUT space-time. The orbits drawn in black are standard orbits with infinite proper time, the orbits in red, blue, and green are geodesically incomplete.crossing one of the horizons r − or r + , it cannot cross this horizon a second time, because ψ(γ) diverges there. At
The complete analytical solutions of the geodesic equations in Kerr-de Sitter and Kerr-anti-de Sitter space-times are presented. They are expressed in terms of Weierstrass elliptic ℘, ζ, and σ functions as well as hyperelliptic Kleinian σ functions restricted to the one-dimensional θ-divisor. We analyse the dependency of timelike geodesics on the parameters of the space-time metric and the test-particle and compare the results with the situation in Kerr space-time with vanishing cosmological constant. Furthermore, we systematically can find all last stable spherical and circular orbits and derive the expressions of the deflection angle of flyby orbits, the orbital frequencies of bound orbits, the periastron shift, and the Lense-Thirring effect.PACS numbers:
The exact solution for the electromagnetic field occuring when the KerrTaub-NUT compact object is immersed (i) in an originally uniform magnetic field aligned along the axis of axial symmetry (ii) in dipolar magnetic field generated by current loop has been investigated. Effective potential of motion of charged test particle around Kerr-Taub-NUT gravitational source immersed in magnetic field with different values of external magnetic field and NUT parameter has been also investigated. In both cases presence of NUT parameter and magnetic field shifts stable circular orbits in the direction of the central gravitating object. Finally we find analytical solutions of Maxwell equations in the external background spacetime of a slowly rotating magnetized NUT star. The star is considered isolated and in vacuum, with monopolar configuration model for the stellar magnetic field.
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