We construct asymptotically flat, static spherically symmetric black holes
with regular centre in $f(R,T)$ gravity coupled to nonlinear electrodynamics
Lagrangian. We obtain generalized metric function of the Bardeen and Hayward
black holes. The null, weak and strong energy conditions of these solutions are
discussed. All the energy conditions hold outside the black hole’s outer event
horizon by appropriated choices of parameters. Quasinormal mode of massive
scalar perturbation is also investigated. Quasinormal frequencies are computed
via the sixth order Wentzel-Kramers-Brillouin (WKB) with Pad’e approximation.
All the imaginary parts of the frequencies are found to be negative. Finally,
we provide an analysis in the eikonal limit.
In this study, we have examined the construction of asymptotically flat, static spherically symmetric black holes with regular centers in the context of $f(R,T)$ gravity coupled to nonlinear electrodynamics Lagrangian. The goal was to obtain the generalized metric function for Bardeen and Hayward black holes.
We have also discussed the null, weak, and strong energy conditions of these solutions. It was found that by appropriately choosing the parameters, all the energy conditions hold outside the black hole’s outer event horizon.
In addition to analyzing the energy conditions, we have investigated the quasinormal mode of massive scalar perturbation in these black holes. The quasinormal frequencies were computed using the sixth-order Wentzel-Kramers-Brillouin (WKB) method with Padé approximation. Notably, all the imaginary parts of the frequencies were found to be negative.
Finally, we have provided an analysis in the eikonal limit. This analysis helps us understand the behavior of waves as they approach the black hole’s horizon.
Future Roadmap
Building on this research, there are several potential challenges and opportunities on the horizon:
1. Generalization to other black hole geometries
While this study focused on asymptotically flat, static spherically symmetric black holes, there is room for examining other geometries. Generalizing these findings to more complex black hole configurations could provide valuable insights into the behavior of black holes in different spacetime backgrounds.
2. Exploration of alternative gravity theories
The $f(R,T)$ gravity framework used in this study offers a fascinating approach to describing black holes. Exploring other alternative gravity theories and understanding their implications for black hole physics could lead to innovative results and potential breakthroughs in our understanding of gravity.
3. Investigation of other perturbation modes
While this study focused on the quasinormal mode of massive scalar perturbation, exploring the behavior of other perturbation modes, such as gravitational or electromagnetic perturbations, could provide a more complete understanding of the dynamics near black holes.
4. Experimental verification
One of the essential steps in validating the theoretical findings is experimental verification. Collaborating with observational astronomers and designing experiments to test the predictions made based on the constructed black hole solutions would provide further confirmation of the validity of these models.
In conclusion, this study has made significant progress in constructing and analyzing asymptotically flat, static spherically symmetric black holes in the context of $f(R,T)$ gravity coupled to nonlinear electrodynamics. The future roadmap outlined above presents exciting directions for further research and exploration in black hole physics.