Holographic Einstein ring of charged black holes in Kalb-Ramond field

<p indent="0mm">This study investigates the Einstein rings of charged black holes in the Kalb-Ramond (KR) field based on AdS/CFT correspondence. When the wave source is fixed on the AdS boundary, we can obtain the corresponding response function on the other side of the boundary. Utilizing a specialized optical system equipped with a convex lens, we can capture the holographic image of Einstein rings of the black hole on a screen. It is found that the variation in the observer’s position leads to a transformation of the image on the screen from an axisymmetric ring to an arc and finally to a single luminous point. We also found that the radius of the Einstein ring decreases as the Lorentz breaking parameter <inline-formula id="INLINE80"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">ℓ</mml:mi></mml:math></inline-formula> increases. As the temperature increases, the radius of the Einstein ring decreases. As the chemical potential increases, the radius of the Einstein ring decreases. From the perspective of geometric optics, we also discover the photon ring of the black hole. Numerical results indicate that the incidence angle of the photon ring is consistent with that of the Einstein ring, verifying the effectiveness of studying Einstein rings through wave optics.