Distinguishing rotating naked singularities from Kerr-like wormholes by their deflection angles of massive particles

Abstract

We study the gravitational deflection of relativistic massive particles by Janis-Newman-Winicour (JNW) spacetimes (also known as a rotating source with a surface-like naked singularity), and a rotating Kerr-like wormholes. Based on the recent article [K. Jusufi, Phys.Rev. D 98, 064017 (2018)], we extend some of these results by exploring the effects of naked singularity and Kerr-like objects on the deflection of particles. We start by introducing coordinate transformation leading to an isotropic line element which gives the refraction index of light for the corresponding optical medias. On the other hand, the refraction index for massive particles is found by considering those particles as a de Broglie wave packets. To this end, we apply the Gauss-Bonnet theorem to the isotropic optical metrics to find the deflection angles. Our analysis shows that, in the case of the JNW spacetime the deflection angle is affected by the parameter 0 < γ < 1, similarly, we find that the deformation parameter λ affects the deflection angle in the case of Kerr-like wormholes. In addition to that, we presented a detailed analysis of the deflection angle by means of the Hamilton-Jacobi equation that lead to the same results. As a special case of our results the deflection angle of light is recovered. Finally, we point out that the deflection of particles by Kerr-like wormholes is stronger compared to JNW spacetime, in particular this difference can be used to shed some light from observational point of view in order to distinguish the two spacetimes.

Gravitational deflection of massive particles in Schwarzschild-de Sitter spacetime

“…which matches well with the result of the Schwarzschild deflection angle of massive particles up to the second order via other approaches [58][59][60][61][62][64][65][66][67][68][69][70][71]. In the limit v 0 → 1, Eq.…”

“…Here, the conserved quantities E and L may be [49,[58][59][60][61][62][63], respectively, where v 0 represents the initial velocity of a massive particle, and the impact parameter b is defined by L/E = v 0 b, which is consistent with the definition b ≡ L/E for the case of light (v 0 = 1) [34]. Notice that the source and the observer situated in the extensive and essentially flat region between the Schwarzschild and de Sitter geometries are still very far away from the gravitational lens, although the value of r cannot exceed the de Sitter radius (r d S = √ 3/Λ).…”

Wormhole solutions in f(R) gravity

“…The wormhole solution by Morris and Thorne 3 was based on the standard general relativity (GR) and presented significant improvement on the earlier wormhole geom-etry such as Wheeler wormholes 19,20 , Kerr wormholes 21,22 and Schwarzschild wormholes 23,24 . Lemos et al 25 have presented a systematic review of wormhole solutions and matched the interior solution to the unique exterior vacuum solution using Einstein's equations whereas Hayward 26 reviewed the dynamic processes that involves wormholes and suggested the wormhole thermodynamics.…”

Observational signatures of strongly naked singularities: image of the thin accretion disk

“…[36][37][38], becoming most famous in the literature in the form derived by Janis, Newman and Winicour. The optical properties of the Janis-Newman-Winicour (JNW) solution were investigated in detail in a series of works [39][40][41][42][43][44], including the gravitational lensing and the relativistic images that can arise in its spacetime. The solution is characterized by two physically distinct regimes depending on its scalar charge to mass ratio called weakly and strongly naked singularities.…”