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Gravitational Lensing Using Werner's Method in Cartesian-like Coordinates

Zonghai Li

Apr 30, 2024

9 pages

e-Print:

2404.19658 [gr-qc]

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Abstract: (arXiv)

The Gibbons-Werner method for calculating deflection angles using the Gauss-Bonnet theorem and optical/Jacobi metric has become widely popular in recent years. Werner extended this method to stationary spacetimes, where the optical/Jacobi metric takes the form of a Finsler metric of Randers type, by adopting an osculating Riemannian metric. Werner's method is significant as it provides a concise expression for the deflection angle, retains applicability for gravitational lensing in Finsler geometry beyond the Randers type, and has the potential to stimulate widespread application of Finsler geometry across diverse fields. However, because of the cumbersome calculations required in Werner's method using conventional coordinates

(r,\phi)

, it has not been widely adopted. The aim of this paper is to alleviate the computational burden associated with Werner's method. To this end, we introduce Cartesian-like coordinates

(X,Y)

to construct the osculating Riemannian metric and calculate the deflection angle using the Gauss-Bonnet theorem. We illustrate the current method with examples of the deflection of massive particles in Kerr spacetime, rotating Bardeen (Hayward) regular spacetime, and Teo rotating wormhole spacetime, respectively.

Note:

9 pages, 2 figures. To appear in Phys. Rev. D (2025)

References(97)

Figures(2)

[1]

Applications of the Gauss-Bonnet theorem to gravitational lensing

- Class.Quant.Grav. 25 (2008) 235009
•
e-Print:
- 0807.0854
•
DOI:
- 10.1088/0264-9381/25/23/235009

[2]

Zur Gravitationstheorie

Hermann Weyl

- Annalen Phys. 359 (1917) 18, 117-145
•
DOI:
- 10.1002/andp.19173591804

[3]

Ray Optics, Fermat’s Principle, and Applications to General Relatively

V. Perlick

[4]

Gravitational lensing in the Kerr-Randers optical geometry

M.C. Werner
(
- Tokyo U., IPMU
)

- Gen.Rel.Grav. 44 (2012) 3047-3057
•
e-Print:
- 1205.3876
•
DOI:
- 10.1007/s10714-012-1458-9

[5]

Gravitomagnetic bending angle of light with finite-distance corrections in stationary axisymmetric spacetimes

- Phys.Rev.D 96 (2017) 10, 104037
•
e-Print:
- 1704.05615
•
DOI:
- 10.1103/PhysRevD.96.104037

[6]

Uber Finslersche Raumee (Wolf, Munchen,)

T. Nazım

[7]

Light Deflection with Torsion Effects Caused by a Spinning Cosmic String

Kimet Jusufi
(
- Stip U.
)

- Eur.Phys.J.C 76 (2016) 6, 332
•
e-Print:
- 1605.02781
•
DOI:
- 10.1140/epjc/s10052-016-4185-7

[8]

Gravitational Lensing by Rotating Wormholes

Kimet Jusufi
(
- State U., Tetova and
- Skopje U.
)
,
Ali Övgün
(
- Geneva U. and
- CERN
)

- Phys.Rev.D 97 (2018) 2, 024042
•
e-Print:
- 1708.06725
•
DOI:
- 10.1103/PhysRevD.97.024042

[9]

Deflection of light by rotating regular black holes using the Gauss-Bonnet theorem

Kimet Jusufi
(
- State U., Tetova and
- Skopje U.
)
,
Ali Övgün
(
)
,
Joel Saavedra
(
- Valparaiso U., Catolica
)
,
Yerko Vásquez
(
- La Serena U.
)
,
P.A. González
(
- Diego Portales U.
)

- Phys.Rev.D 97 (2018) 12, 124024
•
e-Print:
- 1804.00643
•
DOI:
- 10.1103/PhysRevD.97.124024

[10]

Effect of Lorentz Symmetry Breaking on the Deflection of Light in a Cosmic String Spacetime

Kimet Jusufi
(
- State U., Tetova and
- Skopje U.
)
,
Izzet Sakallı
(
- Eastern Mediterranean U.
)
,
Ali Övgün
(
- Eastern Mediterranean U. and
- Valparaiso U., Catolica
)

- Phys.Rev.D 96 (2017) 2, 024040
•
e-Print:
- 1705.06197
•
DOI:
- 10.1103/PhysRevD.96.024040

[11]

Light Deflection by a Rotating Global Monopole Spacetime

Kimet Jusufi
(
- State U., Tetova
)
,
Marcus C. Werner
(
- Kyoto U., Yukawa Inst., Kyoto
)
,
Ayan Banerjee
(
- Jadavpur U.
)
,
Ali Övgün
(
- Eastern Mediterranean U.
)

- Phys.Rev.D 95 (2017) 10, 104012
•
e-Print:
- 1702.05600
•
DOI:
- 10.1103/PhysRevD.95.104012

[12]

Effect of the cosmological constant on the deflection angle by a rotating cosmic string

Kimet Jusufi
(
- State U., Tetova and
- Skopje U.
)
,
Alï Ovgün
(
- Valparaiso U., Catolica and
- Eastern Mediterranean U.
)

- Phys.Rev.D 97 (2018) 6, 064030
•
e-Print:
- 1712.01771
•
DOI:
- 10.1103/PhysRevD.97.064030

[13]

Light Deflection by a Quantum Improved Kerr Black Hole Pierced by a Cosmic String

- Int.J.Geom.Meth.Mod.Phys. 16 (2019) 08, 1950116
•
e-Print:
- 1707.02824
•
DOI:
- 10.1142/S0219887819501160

[14]

Shadow and Weak Deflection Angle of a Black Hole in Nonlocal Gravity

Qi-Ming Fu
(
- Shenyang, Northeast U. Tech. and
- Shaanxi U. Tech.
)
,
Shao-Wen Wei
(
- Lanzhou U.
)
,
Li Zhao
(
- Lanzhou U.
)
,
Yu-Xiao Liu
(
- Lanzhou U.
)
,
Xin Zhang
(
- Shenyang, Northeast U. Tech.
)

- Universe 8 (2022) 7, 341,
- Universe 8 (2022) 341
•
e-Print:
- 2203.05157
•
DOI:
- 10.3390/universe8070341

[15]

Effect of the Quintessential Dark Energy on Weak Deflection Angle by Kerr-Newmann Black Hole

W. Javed
(
- U. Educ., Lahore
)
,
J. Abbas
(
- U. Educ., Lahore
)
,
A. Övgün
(
- Valparaiso U., Catolica and
- Eastern Mediterranean U.
)

- Annals Phys. 418 (2020) 168183
•
e-Print:
- 2007.16027
•
DOI:
- 10.20944/preprints201906.0124.v1

[16]

Deflection angle of light for an observer and source at finite distance from a rotating wormhole

- Phys.Rev.D 98 (2018) 4, 044047
•
e-Print:
- 1806.05360
•
DOI:
- 10.1103/PhysRevD.98.044047

[17]

Deflection angle of light for an observer and source at finite distance from a rotating global monopole

- Phys.Rev.D 99 (2019) 12, 124030
•
e-Print:
- 1811.01739
•
DOI:
- 10.1103/PhysRevD.99.124030

[18]

Light deflection by Damour-Solodukhin wormholes and Gauss-Bonnet theorem

Ali Övgün
(
- Valparaiso U., Catolica and
- Eastern Mediterranean U. and
- Fresno State and
- Stanford U., ITP
)

- Phys.Rev.D 98 (2018) 4, 044033
•
e-Print:
- 1805.06296
•
DOI:
- 10.1103/PhysRevD.98.044033

[19]

Shadow cast and Deflection angle of Kerr-Newman-Kasuya spacetime

- JCAP 10 (2018) 041
•
e-Print:
- 1807.00388
•
DOI:
- 10.1088/1475-7516/2018/10/041

[20]

Weak gravitational lensing by Kerr-MOG black hole and Gauss–Bonnet theorem

- Annals Phys. 411 (2019) 167978
•
e-Print:
- 1806.06453
•
DOI:
- 10.1016/j.aop.2019.167978

[21]

Finite distance corrections to the light deflection in a gravitational field with a plasma medium

Gabriel Crisnejo
(
- Cordoba U.
)
,
Emanuel Gallo
(
- Cordoba U. and
- Buenos Aires, CONICET
)
,
Adam Rogers
(
- Brandon U.
)

- Phys.Rev.D 99 (2019) 12, 124001
•
e-Print:
- 1807.00724
•
DOI:
- 10.1103/PhysRevD.99.124001

[22]

Shadow cast and deflection of light by charged rotating regular black holes

- Phys.Rev.D 100 (2019) 12, 124024
•
e-Print:
- 1912.05154
•
DOI:
- 10.1103/PhysRevD.100.124024

[23]

Gravitational deflection of light and shadow cast by rotating Kalb-Ramond black holes

Rahul Kumar
(
- Jamia Millia Islamia
)
,
Sushant G. Ghosh
(
- Jamia Millia Islamia and
- KwaZulu Natal U.
)
,
Anzhong Wang
(
- Baylor U. and
- Zhejiang U. Tech.
)

- Phys.Rev.D 101 (2020) 10, 104001
•
e-Print:
- 2001.00460
•
DOI:
- 10.1103/PhysRevD.101.104001

[24]

Shadow and deflection angle of rotating black hole in asymptotically safe gravity

Rahul Kumar
(
- Jamia Millia Islamia
)
,
Balendra Pratap Singh
(
- Jamia Millia Islamia
)
,
Sushant G. Ghosh
(
- Jamia Millia Islamia and
- KwaZulu Natal U.
)

- Annals Phys. 420 (2020) 168252
•
e-Print:
- 1904.07652
•
DOI:
- 10.1016/j.aop.2020.168252

[25]

Shadow and Deflection Angle of Rotating Black Holes in Perfect Fluid Dark Matter with a Cosmological Constant

Sumarna Haroon
(
- NUST, Islamabad and
- Waterloo U.
)
,
Mubasher Jamil
(
- NUST, Islamabad
)
,
Kimet Jusufi
(
- State U., Tetova and
- Skopje U.
)
,
Kai Lin
(
- Chinese U. of Geoscience, Wuhan and
- U. Sao Paulo (main)
)
,
Robert B. Mann
(
- Waterloo U.
)

- Phys.Rev.D 99 (2019) 4, 044015
•
e-Print:
- 1810.04103
•
DOI:
- 10.1103/PhysRevD.99.044015

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