TY - JOUR

T1 - Gravitational lensing under the effect of Weyl and bumblebee gravities

T2 - Applications of Gauss–Bonnet theorem

AU - Övgün, Ali

AU - Jusufi, Kimet

AU - Sakallı, İzzet

N1 - Funding Information:
We wish to thank the Editor and anonymous Referee for their valuable comments and suggestions. This work is supported by Comisión Nacional de Ciencias y Tecnología of Chile (CONICYT) through FONDECYT Grant No. 3170035 (A. Ö.).
Publisher Copyright:
© 2018 Elsevier Inc.

PY - 2018/12

Y1 - 2018/12

N2 - In this paper, we use the Gauss–Bonnet theorem to obtain the deflection angle by the photons coupled to Weyl tensor in a Schwarzschild black hole and Schwarzschild-like black hole in bumblebee gravity in the weak limit approximation. To do so, we first calculate the corresponding optical metrics, and then we find the Gaussian curvature to use in Gauss–Bonnet theorem, which is first done by Gibbons and Werner. Hence, in the leading order terms we show the deflection angle, that is affected by the coupling between the photon and Weyl tensor, and there is a deviation from the deflecting angle as compared with Schwarzschild black hole with Schwarzschild-like black hole in bumblebee gravity. Moreover, we investigate the deflection angle by Einstein–Rosen type wormhole in Weyl gravity and in bumblebee gravity. Interestingly, the deflection angle by Einstein–Rosen type wormhole in bumblebee gravity is found as larger than the deflection angle by Einstein–Rosen type wormhole in Weyl gravity.

AB - In this paper, we use the Gauss–Bonnet theorem to obtain the deflection angle by the photons coupled to Weyl tensor in a Schwarzschild black hole and Schwarzschild-like black hole in bumblebee gravity in the weak limit approximation. To do so, we first calculate the corresponding optical metrics, and then we find the Gaussian curvature to use in Gauss–Bonnet theorem, which is first done by Gibbons and Werner. Hence, in the leading order terms we show the deflection angle, that is affected by the coupling between the photon and Weyl tensor, and there is a deviation from the deflecting angle as compared with Schwarzschild black hole with Schwarzschild-like black hole in bumblebee gravity. Moreover, we investigate the deflection angle by Einstein–Rosen type wormhole in Weyl gravity and in bumblebee gravity. Interestingly, the deflection angle by Einstein–Rosen type wormhole in bumblebee gravity is found as larger than the deflection angle by Einstein–Rosen type wormhole in Weyl gravity.

KW - Classical black holes

KW - Deflection angle

KW - Gauss–Bonnet theorem

KW - Gravitational lensing

KW - Relativity and gravitation

UR - http://www.scopus.com/inward/record.url?scp=85055720852&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2018.10.012

DO - 10.1016/j.aop.2018.10.012

M3 - Article

AN - SCOPUS:85055720852

SN - 0003-4916

VL - 399

SP - 193

EP - 203

JO - Annals of Physics

JF - Annals of Physics

ER -