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

This paper 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 for both black holes (BHs) and compare their observational impacts. The horizon radius, photon radius and the critical impact parameter for KR BHs decrease with the LV parameter [Formula: see text]. In contrast, they remain independent of the BM parameter [Formula: see text] and have values the same as those for Schwarzschild BH. Their qualitative and quantitative variations with [Formula: see text] are illustrated for KR BH. Our study reveals that the observed intensity for static and infalling accretions peaks at the critical impact parameter. We find that a KR BH is brighter than a Schwarzschild or BM BH for static as well as infalling accretion. The BM BH, on the other hand, is brighter than a Schwarzschild BH when the accretion is static but becomes darker for an infalling accretion. The shadow’s size, independent of the accretion type, is smaller for a KR BH. Our investigation into quasinormal modes (QNMs) with the help of the [Formula: see text]th order Padé averaged WKB method 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 Schwarzschild or BM BHs for scalar and electromagnetic perturbations. GWs emitted by BM BHs have lower frequency and decay slower than those emitted by Schwarzschild BHs for scalar perturbation, whereas the frequency is higher for electromagnetic perturbation. We then study the graybody 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 Schwarzschild BH. It also reveals that the transmission probability decreases with [Formula: see text] and [Formula: see text]. 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 finally try to differentiate between KR and BM BHs based on their observational signatures in the weak gravitational lensing. We obtain higher-order corrections in the deflection angle and graphically illustrate the impact of [Formula: see text] and [Formula: see text]. We observe that a light ray gets deflected most from its path when passing by a Schwarzschild 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.