Analytic treatment of complete and incomplete geodesics in Taub-NUT space-times

Abstract

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

On the NUT–Born–Infeld-Λspacetime

“…It would be interesting to classify the allowed orbits in the effective potentials in a meticulous way (see for instance [32]), as well as the behavior of the effective potential with varying cosmological constant and the trajectories that arise are worth of a thorough study. The interesting parameters included in the NUT-BI-Λ solution makes the thermodynamics of the system be also a promising subject that however is beyond the scope of this work.…”

Test particle motion in the Born-Infeld black hole

“…It follows a < 0 since k ≥ 0. The turning points where Θ ξ vanishes define the angles of two cones and the motion of test particles is confined to this region; it has been pointed out before that a similar feature appears in Taub-NUT and Kerr spacetimes [29,30]. In the special case when ∆ g vanishes, the motion takes place on a plane, as exemplified by the orbits of only electrically charged or neutral particles in a RN spacetime.…”

Twisted black hole is Taub-NUT

“…Note that the Taub-NUT solution is indeed known to be geodesically incomplete (see, e.g., [14,15]. However, see [16]), although it does not have a curvature singularity.…”

“…Not all geodesics are complete due to these wire singularities [14,15]. The wire singularities can nevertheless be removed by introducing new coordinate patches and compactifying the temporal coordinate so that the topology of the spacetime becomes R × S 3 [13].…”