Strong Deflection Gravitational Lensing for the Photons Coupled to the Weyl Tensor in a Conformal Gravity Black Hole

In the present paper, strong deflection gravitational lensing is studied in a conformal gravity black hole. With the help of geometric optics limits, we have formulated the light cone conditions for the photons coupled to the Weyl tensor in a conformal gravity black hole. It is explicitly found that strong deflection gravitational lensing depends on the coupling with the Weyl tensor, the polarization directions, and the black hole configuration parameters. We have applied the results of the strong deflection gravitational lensing to the supermassive black holes <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>g</mi><mi>r</mi><msup><mi>A</mi><mo>*</mo></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><msup><mn>87</mn><mo>*</mo></msup></mrow></semantics></math></inline-formula> and studied the possibility of encountering quantum improvement. It is not practicable to recognize similar black holes through the strong deflection gravitational lensing observables in the near future, except for the possible size of the black hole’s shadow. We also notice that by directly adopting the constraint of the measured shadow of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><msup><mn>87</mn><mo>*</mo></msup></mrow></semantics></math></inline-formula>, the quantum effect demands immense care.