Exploring Weak Gravitational Lensing Effects by a Regular Black Hole

Authors

  • A. K. Durrani Department Fisika, FMIPA, Universitas Indonesia, Depok, 16424, Indonesia
  • H. S. Ramadhan Department Fisika, FMIPA, Universitas Indonesia, Depok, 16424, Indonesia

DOI:

https://doi.org/10.21009/SPEKTRA.092.02

Keywords:

gravitational lensing, regular charged black hole, deflection angle, image positions, magnification

Abstract

Gravitational lensing is one of the physical consequences of Einstein’s general theory of relativity, which has been observationally confirmed. This work aims to study the weak gravitational lensing scenario where the lens is a spherically symmetric, charged-nonsingular black hole that asymptotically behaves as the Reissner-Nordström (RN). The difference exists in the higher-order expansion. Therefore, the metric function of the regular charged black hole is expanded up to the fourth order, and the deflection angle is calculated. The thin lens equation is used, leading to five images: two imaginary and three real images. The exact positions of the images and magnification properties are calculated by providing the physical parameters such as mass, charge, and distances. Our calculation shows that the third image position shifted away from the optical axis. The formalism is applied to the case of a supermassive black hole located at the center of our galaxy with the assumption that it has an electric charge.

References

S. Chandrasekhar, The Mathematical Theory of Black Holes. New York: Oxford University Press, 1998.

T. P. Kling and E. T. Newman, “Spacetime perspective of Schwarzschild lensing,” Physical Review D - Particles, Fields, Gravitation and Cosmology, vol. 61, no. 6, 2000, doi: 10.1103/PHYSREVD.61.064021.

K. S. Virbhadra and G. F. R. Ellis, “Schwarzschild black hole lensing,” Physical Review D - Particles, Fields, Gravitation and Cosmology, vol. 62, no. 8, pp. 1–8, Oct. 2000, doi: 10.1103/PHYSREVD.62.084003.

V. Bozza, S. Capozziello, G. Iovane, and G. Scarpetta, “Strong field limit of black hole gravitational lensing,” Gen Relativ Gravit, vol. 33, no. 9, pp. 1535–1548, 2001, doi: 10.1023/A:1012292927358.

S. Fernando and S. Roberts, “Gravitational lensing by charged black holes,” Gen Relativ Gravit, vol. 34, no. 8, pp. 1221–1230, 2002, doi: 10.1023/A:1019726501344.

E. Ayón-Beato and A. García, “Regular black hole in general relativity coupled to nonlinear electrodynamics,” Phys Rev Lett, vol. 80, no. 23, pp. 5056–5059, 1998, doi: 10.1103/PHYSREVLETT.80.5056.

E. Ayón-Beato and A. García, “New regular black hole solution from nonlinear electrodynamics,” Physics Letters B, 1999. Accessed: Jun. 15, 2024, doi: 10.1016/S0370-2693(99)01038-2.

E. Ayón-Beato and A. Garcia, “Non-Singular Charged Black Hole Solution for Non-Linear Source,” Gen Relativ Gravit, vol. 31, no. 5, pp. 629–633, May 1999, doi: 10.1023/A:1026640911319.

E. Ayón-Beato and A. García, “The Bardeen model as a nonlinear magnetic monopole,” Physics Letters B, 2000. Accessed: Jun. 15, 2024, doi: 10.1016/S0370-2693(00)01125-4

S. Orzuev, F. Atamurotov, A. Abdujabbarov, and A. Abduvokhidov, “Weak gravitational lensing of black hole from T-duality in plasma,” New Astronomy, vol. 105, Jan. 2024, doi: 10.1016/j.newast.2023.102104.

A. Borde, “Open and closed universes, initial singularities, and inflation,” Physical Review D, vol. 50, no. 6, pp. 3692–3702, 1994, doi: 10.1103/PHYSREVD.50.3692.

A. Borde, “Regular black holes and topology change,” Physical Review D - Particles, Fields, Gravitation and Cosmology, vol. 55, no. 12, pp. 7615–7617, 1997, doi: 10.1103/PHYSREVD.55.7615.

V. P. Frolov, “Information loss problem and a `black hole’ model with a closed apparent horizon,” Journal of High Energy Physics, 2014, doi: 10.1007/JHEP05(2014)049.

V. P. Frolov, “Remarks on non-singular black holes,” EPJ Web of Conferences, Aug. 2017, doi: 10.1051/epjconf/201816801001.

R. Carballo-Rubio, F. Di Filippo, S. Liberati, C. Pacilio, and M. Visser, “On the viability of regular black holes,” Journal of High Energy Physics, May 2018, doi: 10.1007/JHEP07(2018)023.

V. P. Frolov, “Notes on non-singular models of black holes,” Physical Review D, Sep. 2016, doi: 10.1103/PhysRevD.94.104056.

V. P. Frolov and A. Zelnikov, “Quantum radiation from an evaporating non-singular black hole,” Physical Review D, Apr. 2017, doi: 10.1103/PhysRevD.95.124028.

R. Izmailov, R. Karimov, and E. R. Zhdanov, “Modified gravity black hole lensing observables in weak and strong field of gravity,” Monthly Notices of the Royal Astronomical Society, 2018, doi: 10.1093/MNRAS/STY3350.

S. Sahu, K. Lochan, and D. Narasimha, “Gravitational lensing by a black hole in effective loop quantum gravity,” Physical Review D, 2015, doi: 10.1103/PhysRevD.91.063001.

A. Bhadra, “Gravitational lensing by a charged black hole of string theory,” Physical Review D, 2003, doi: 10.1103/PhysRevD.67.103009.

F.-Y. Liu, Y.-F. Mai, W. Wu, and Y. Xie, “Probing a regular non-minimal Einstein-Yang-Mills black hole with gravitational lensings,” Physics Letters B, 2019, doi: 10.1016/J.PHYSLETB.2019.06.052.

L. Balart and E. C. Vagenas, “Bardeen regular black hole with an electric source,” Physical Review D - Particles, Fields, Gravitation and Cosmology, vol. 90, no. 12, p. 124045, Dec. 2014, doi: 10.1103/PHYSREVD.90.124045.

J. P. S. Lemos and V. T. Zanchin, “Regular black holes: Electrically charged solutions, Reissner-Nordström outside a deSitter core,” Physical Review D - Particles, Fields, Gravitation and Cosmology, vol. 83, no. 12, Jun. 2011, doi: 10.1103/PHYSREVD.83.124005.

V. Bozza, “Gravitational lensing in the strong field limit,” Physical Review D - Particles, Fields, Gravitation and Cosmology, vol. 66, no. 10, Nov. 2002, doi: 10.1103/PHYSREVD.66.103001.

N. Tsukamoto, “Deflection angle in the strong deflection limit in a general asymptotically flat, static, spherically symmetric spacetime,” Physical Review D, vol. 95, no. 6, Mar. 2017, doi: 10.1103/PHYSREVD.95.064035.

Downloads

Published

2024-07-15

How to Cite

Durrani, A. K., & Ramadhan, H. S. (2024). Exploring Weak Gravitational Lensing Effects by a Regular Black Hole. Spektra: Jurnal Fisika Dan Aplikasinya, 9(2), 75–84. https://doi.org/10.21009/SPEKTRA.092.02