Observational signature of Lorentz violation in Kalb-Ramond field model and Bumblebee model: A comprehensive comparative study

This article is devoted to the comparative study of the effects of the Lorentz symmetry violation (LV) arising in Kalb-Ramond (KR) and Bumblebee (BM) field models. We study optical appearance with accretion, Quasinormal modes, ringdown waveforms, Hawking radiation, and weak gravitational lensing. The horizon radius, photon radius, and the critical impact parameter for KR BHs decrease with the LV parameter $\a$. In contrast, they remain independent of the BM parameter $\b$ and have values the same as those for \s BH. We find that a KR BH is brighter than a \s or BM BH for static and infalling accretion. The BM BH, on the other hand, is brighter than a \s BH when the accretion is static but becomes darker for an infalling accretion. Our investigation into quasinormal modes (QNMs) and ringdown waveforms provides deeper insight into the difference in observational imprints of LV parameters. It reveals that GWs emitted by KR BHs have larger frequencies and decay faster than those emitted by \s or BM BHs for scalar and electromagnetic perturbations. We then study the greybody factor (GF) and power emitted for both BHs. The Hawking temperature is higher for a KR BM and lower for a BM BH than a \s BH. It also reveals that the transmission probability decreases with $\a$ and $\b$. A comparison of GFs for KR and BM BHs reveals that the transmission probability is higher for BM BH. We also study the effect of LV on the power emitted in the form of Hawking radiation. Power received by an asymptotic observer is larger for a KR BH. We obtain higher-order corrections in the deflection angle and graphically illustrate the impact of $\a$ and $\b$. We observe that a light ray gets deflected most from its path when passing by a \s BH, and the deflection is least when it passes by a KR BH. Our study conclusively shows that we can differentiate between KR and BM BHs based on astrophysical observations.