Lensing and Relativistic Images in Black Hole Geometries

Sammanfattning

This thesis presents a comprehensive study of strong field gravitational lensing near the photon sphere of black holes, where two infinite sequences of relativistic images form on each side of the black hole due to extreme light bending. Focusing on the supermassive black hole SgrA∗ as a prototype, we analytically and numerically investigate the lensing characteristics on the equatorial plane including angular positions, magnifications, def lection angles, strong deflection limit coefficients, lensing observables, and time delays for Schwarzschild, Reissner-Nordstr¨ om (RN) and Kerr black hole geometries. The results show that the photon sphere radius xp shrinks with charge (1.486 at q = 0.1 to 1 at q = 0.5), while in Kerr black holes, it ranges asymmetrically from 2 (retrograde, a = −0.5) to 0.5 (prograde, a = 0.5), merging with the horizon in the extremal case a = 0.5. Lensing observables exhibit clear geometric dependencies; RN charge reduces deflection angles and shifts images inward with respect to the Schwarzschild case, while Kerr spin induces strong asymmetry, with prograde photons experiencing weaker bending (ˆ α1 down to 2π+21.38µas) and shorter time delays (2.88 min vs. 10.09 min retrograde). Magnifications remain faint (µ1 ≈ 10−12) but show spin-/charge-driven variations, including brighter prograde images (µ1 ≈ 10−11). These results provide measurable signatures (image separations ≈ 7µas, flux ratio trends) to distinguish static, charged, and spinning black holes via observations.