arXiv:2409.05897v1 Announce Type: new
Abstract: In this paper, we address a theoretical investigation of the gravitational lensing phenomenon within the space-time framework of a holonomy-corrected spherically symmetric black hole (BH), incorporating both ordinary and phantom global monopoles. Our focus lies on the analysis of null geodesics within this black hole background, examining the influence of ordinary and phantom global monopoles on the effective potential of null geodesics of the system. Afterwards, we derive analytical expressions for the deflection angle of photon light, considering weak field limit. The obtain expressions are presented up to the second order of the Loop Quantum Gravity parameter, enabling a thorough examination of the impact of ordinary and phantom global monopoles on the deflection angle.
Roadmap for Readers: Investigating Gravitational Lensing in a Holonomy-Corrected Spherically Symmetric Black Hole
Introduction
In this paper, we delve into a theoretical investigation of the gravitational lensing phenomenon within the space-time framework of a holonomy-corrected spherically symmetric black hole. We aim to understand how the presence of both ordinary and phantom global monopoles affects the null geodesics and the deflection angle of photon light in this black hole background.
Analysis of Null Geodesics
We start by analyzing the behavior of null geodesics within the black hole background. Our focus is to determine how the ordinary and phantom global monopoles influence the effective potential of these geodesics. By examining the influence of these monopoles, we can gain insights into the overall structure of the black hole geometry and understand their impact on the deflection of light.
Derivation of Deflection Angle
Next, we derive analytical expressions for the deflection angle of photon light in the presence of ordinary and phantom global monopoles. This analysis is carried out under the assumption of a weak field limit, allowing us to approximate the deflection angle within a certain range.
Second-Order Loop Quantum Gravity Parameter
We go a step further in our analysis by presenting the analytical expressions for the deflection angle up to the second order of the Loop Quantum Gravity parameter. By doing so, we enable a more comprehensive examination of the impact of ordinary and phantom global monopoles on the deflection angle. This higher-order analysis provides a more accurate understanding of the behavior of light in the vicinity of the black hole.
Challenges and Opportunities
While our investigation presents valuable insights into gravitational lensing in a holonomy-corrected spherically symmetric black hole, there are certain challenges and opportunities that lie ahead.
- Quantum Gravity Complexity: The inclusion of the Loop Quantum Gravity parameter adds complexity to the analysis, making it challenging to obtain exact solutions. Further research is needed to explore the full quantum gravity implications in the context of gravitational lensing.
- Data Validation: Experimental validation of the derived analytical expressions and predictions is crucial. Future observational studies and data analysis can help confirm or refute the influence of ordinary and phantom global monopoles on the deflection angle.
- Broader Applicability: Expanding the scope of this investigation to other modified gravity theories and alternative black hole models can provide a broader context for understanding the behavior of light in extreme gravitational environments.
- Theoretical Extensions: Building upon this work, exploring the implications of other exotic matter distributions and their impact on gravitational lensing could enhance our understanding of the underlying physics.
Conclusion
Through our theoretical investigation, we have gained valuable insights into the gravitational lensing phenomenon in a holonomy-corrected spherically symmetric black hole. By analyzing null geodesics and deriving analytical expressions for the deflection angle, we have highlighted the influence of ordinary and phantom global monopoles. Challenges and opportunities lie ahead in understanding the full quantum gravity implications, validating predictions, expanding the scope, and exploring further theoretical extensions. Continued research in this area holds promise for advancing our understanding of gravity and the behavior of light in extreme astrophysical scenarios.