Weak field deflection angle and analytical parameter estimation of the Lorentz-violating Bumblebee parameter through the black hole shadow using EHT data

Abstract

We explored how the Lorentz symmetry breaking parameter $\ell$ affects the Reissner-Nordstöm BH solution in the context of weak field deflection angle, and the black hole shadow. We aim to derive the general expression for the weak deflection angle using the non-asymptotic version of the Gauss-Bonnet theorem, and we presented a way to simplify the calculations under the assumption that the distance of the source and the receiver are the same. \textcolor{black}{Through the Solar System test, $\ell$ is constrained from around $-10^{-9}$ orders of magnitude to $0$, implying challenging detection of $\ell$ through the deflection of light rays from the Sun.} We also studied the black hole shadow in an analytic way, where we applied the EHT results under the far approximation in obtaining an estimate expression for $\ell$. Using the realistic values of the black hole mass and observer distance for Sgr. A* and M87*, it was shown that $M/r_{\mathrm{o}}\ne 1$ is satisfied, implying the relevance and potential promise of the spontaneous Lorentz symmetry breaking parameter's role on the shadow radius uncertainties as measured by the EHT. \textcolor{black}{We find constraints for $\ell$ to be negatively valued, where the upper and lower bounds are $\sim -1.94$ and $\sim -2.04$, respectively.

7 pages. Published version

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• Weak Gravitational Lensing in Ricci-Coupled Kalb-Ramond Bumblebee Gravity: Global Monopole and Axion-Plasmon Medium Effects
• Charged black holes in Kalb-Ramond gravity: Weak Deflection Angle, Shadow cast, Quasinormal Modes and Neutrino annihilation
• On the analytic generalization of particle deflection in the weak field regime and shadow size in light of EHT constraints for Schwarzschild-like black hole solutions
• Multimodal signatures of asymptotic (A)dS Kalb-Ramond black holes: Constraints through the shadow, weak deflection angle, and topological photon spheres
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• Regular Black Hole Models in the Transition from Baryonic Matter to Quark Matter
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• Boson Stars in Bumblebee Gravity and Their Gravitational Waveforms from Extreme-Mass-Ratio Inspirals
• Periodic orbits and gravitational waveforms of black holes in bumblebee gravity
• Analytical approach for calculating shadow of dynamical black hole
• Lorentz-violating modifications to particle dynamics, thermodynamics and vacuum energy in bumblebee gravity