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

¹ Dipartimento di Fisica “E.R. Caianiello”, Università degli Studi di Salerno - Via Giovanni Paolo II, 132, 84084 Fisciano (SA), Italy
² Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Salerno, Sezione di Napoli - Via Giovanni Paolo II, 132, 84084 Fisciano (SA), Italy
³ Physics Department, Mapúa University - 658 Muralla St., Intramuros, Manila 1002, Philippines
⁴ Physics Department, Eastern Mediterranean University - Famagusta, 99628 North Cyprus via Mersin 10, Turkiye

Received: 23 August 2024
Accepted: 31 October 2024

Abstract

We explored how the Lorentz symmetry breaking parameter ℓ 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. Through the Solar System test, ℓ is constrained from around orders of magnitude to 0, implying challenging detection of ℓ 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 ℓ. Using the realistic values of the black hole mass and observer distance for Sgr. A* and M87*, it was shown that 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. We find constraints for ℓ to be negatively valued, where the upper and lower bounds are ∼ - 1.94 and ∼ - 2.04, respectively.