We investigate quasitopological black holes in $(2+1)$ dimensions in the
context of electromagnetic-generalized-quasitopological-gravities (EM-GQT). For
three different families of geometries of quasitopological nature, we study the
causal structure and their response to a probe scalar field. To linear order,
we verify that the scalar field evolves stably, decaying in different towers of
quasinormal modes. The studied black holes are either charged geometries
(regular and singular) or a regular Ba~nados-Teitelboim-Zanelli (BTZ)-like
black hole, both coming from the EM-GQT theory characterized by nonminimal
coupling parameters between gravity and a background scalar field. We calculate
the quasinormal modes applying different numerical methods with convergent
results between them. The oscillations demonstrate a very peculiar structure
for charged black holes: in the intermediate and near extremal cases, a
particular scaling arises, similar to that of the rotating BTZ geometry, with
the modes being proportional to the distance between horizons. For the single
horizon black hole solution, we identify the presence of different quasinormal
families by analyzing the features of that spectrum. In all three considered
geometries, no instabilities were found.
Based on our investigation, we have concluded that the quasitopological black holes in $(2+1)$ dimensions in the context of electromagnetic-generalized-quasitopological-gravities (EM-GQT) exhibit stable evolution of a probe scalar field. We have studied three different families of quasitopological geometries and have found that the scalar field decays in different towers of quasinormal modes.
The black holes we have examined can be classified as either charged geometries (regular and singular) or a regular Bañados-Teitelboim-Zanelli (BTZ)-like black hole. These black holes are derived from the EM-GQT theory, which includes nonminimal coupling parameters between gravity and a background scalar field.
In our calculations of the quasinormal modes, we have employed various numerical methods, all yielding convergent results. The oscillations of the modes in charged black holes exhibit a unique structure. In the intermediate and near extremal cases, a scaling proportional to the distance between horizons emerges, similar to that observed in the rotating BTZ geometry.
For the single horizon black hole solution, we have identified the presence of different quasinormal families by analyzing the characteristics of the spectrum. Importantly, we did not find any instabilities in any of the three considered geometries.
Future Roadmap
Challenges:
- Further investigation is needed to understand the causal structure and response of other fields, such as electromagnetic fields, to these quasitopological black holes in EM-GQT theory. The study of other probe fields may reveal additional insights and properties.
- Exploring the thermodynamic properties of these black holes can provide valuable information about their entropy, temperature, and thermodynamic stability. This analysis could involve studying thermodynamic quantities and phase transitions.
- Investigating the stability of these black holes under perturbations beyond linear order could uncover additional behavior and help to determine their long-term evolution.
Opportunities:
- The peculiar scaling observed in the oscillations of charged black holes could lead to new understandings of their underlying physical mechanisms. Further exploration of this scaling effect and its implications may offer insights into the connection between charge and geometry.
- The identification of different quasinormal families in the single horizon black hole solution presents an opportunity for studying the distinct characteristics and dynamics of these families. This information could contribute to a deeper understanding of black hole spectra in general.
- Extending the study to higher dimensions and different theories of gravity could provide valuable comparisons and insights into the behavior of quasitopological black holes across different contexts. Such investigations could include theories with additional matter fields or modified gravity theories.
In conclusion, the examination of quasitopological black holes in $(2+1)$ dimensions in the context of electromagnetic-generalized-quasitopological-gravities (EM-GQT) has revealed stable evolution and unique characteristics. While there are still challenges to address and opportunities to explore, this research lays the foundation for further expanding our understanding of these intriguing black hole solutions.
Reference:
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