https://doi.org/10.1140/epjc/s10052-019-6557-2
Regular Article - Theoretical Physics
Distinguishing rotating naked singularities from Kerr-like wormholes by their deflection angles of massive particles
1
Physics Department, State University of Tetovo, Ilinden Street nn, 1200, Tetovo, Macedonia
2
Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University, Arhimedova 3, 1000, Skopje, Macedonia
3
Astrophysics and Cosmology Research Unit, University of KwaZulu Natal, Private Bag X54001, Durban, 4000, South Africa
4
Faculty of Physics, St. Kliment Ohridski University of Sofia, 5 James Bourchier Boulevard, 1164, Sofia, Bulgaria
5
Department of Physics, Biophysics and Roentgenology, Faculty of Medicine, St. Kliment Ohridski University of Sofia, 1, Kozyak Str., 1407, Sofia, Bulgaria
* e-mail: ayan_7575@yahoo.co.in
Received:
4
October
2018
Accepted:
3
January
2019
Published online:
16
January
2019
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 (Jusufi in 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 
, similarly, we find that the deformation parameter 
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.
© The Author(s), 2019
