arXiv:2509.00127v1 Announce Type: new
Abstract: We find a Kerr-like black hole solution-a rotating Bumblebee black hole (RBBH) with a Lorentz-violating parameter $ell$ and examine the strong lensing by it. The parameter $ell$ changes the event horizon radius and photon sphere, resulting in a different lensing signature compared to the Kerr black hole of general relativity. Using the strong deflection limit formalism, we compute key observables such as the angular positions of relativistic images, their separation, magnification, and time delays for supermassive black holes Sgr A* and M87*. Our results show that the parameter $ell$ has a profound influence on these observables, with $ell > 0$ suppressing and $ell < 0$ increasing the deflection angle compared to the Kerr case. We compare RBBH observables with those of Kerr black holes, using Sgr A* and M87* as lenses to observe the effect of the Lorentz symmetry-breaking parameter $ell$. For Sgr A*, the angular position $theta_infty$ in $in~(18.25-33.3)~mu as$, while for M87* $in~(13.71-25.02)~mu as$. The angular separation $s$, for supermassive black holes (SMBHs) Sgr A* and M87*, differs significantly, with values ranging $in~(0.005-0.81)~mu as$ for Sgr A* and $in~(0.003-0.6)~mu as$ for M87*. The relative magnitude $r_{text{mag}}$ $in~(3.04-8.15)~mu as$. We also compared the time delays between the relativistic images in the SMBHs and found that RBBH can be quantitatively distinguished from Kerr black holes. Our analysis concludes that, within the 1$sigma$ region, a significant portion of the parameter space agrees with the EHT results of M87* and Sgr A*. This demonstrates the feasibility of utilizing strong gravitational lensing to identify Lorentz symmetry violations in extreme gravity regimes. Weak lensing analysis and Einstein ring observations provide further constraints, producing an upper bound of $ell lesssim mathcal{O}(10^{-6})$.
Future Roadmap
- Further Observational Studies: Conduct additional observational studies using other supermassive black holes as lenses to validate the findings on RBBH and explore potential variations in the lensing signature that could provide deeper insights into Lorentz symmetry violations.
- Theoretical Investigations: Engage in theoretical investigations to understand the implications of the Lorentz-breaking parameter $ell$ on fundamental physical principles and theories, such as quantum gravity, to establish a more comprehensive framework.
- Technological Advancements: Develop advanced technological tools and techniques for better precision in observing and measuring angular positions, separations, magnifications, and time delays of relativistic images from black holes, enabling more accurate validations of the RBBH solution.
- Collaborative Efforts: Foster collaborations between theoretical physicists, observational astronomers, and experts in gravitational lensing to combine expertise and resources for a holistic approach towards understanding and testing the boundaries of general relativity in extreme gravity regions.
Potential Challenges:
- Data Interpretation: Address challenges in interpreting observational data due to uncertainties, noise, and external influences that may impact the accuracy of measurements and conclusions drawn from the lensing observations.
- Theoretical Consistency: Ensure consistency between theoretical predictions and observational results, resolving any discrepancies that may arise and refining the theoretical framework to accommodate new findings on Lorentz symmetry violations.
- Resource Allocation: Secure adequate resources and funding for continued research efforts, technological developments, and collaborative initiatives aimed at advancing our understanding of extreme gravity phenomena and testing the limits of general relativity.
In conclusion, the exploration of rotating Bumblebee black hole solutions and the impact of Lorentz violations on strong gravitational lensing present exciting avenues for future research, with the potential to revolutionize our understanding of fundamental physical laws and the nature of spacetime in extreme cosmic environments.