“Static Black Holes with Scalar Hair in Modified General Relativity”
arXiv:2403.15537v1 Announce Type: new
Abstract: Static black holes in general relativity modified by a linear scalar coupling to the Gauss-Bonnet invariant always carry hair. We show that the same mechanism that creates the hair makes it incompatible with a cosmological horizon. Other scalar-tensor models do not have this problem when time-dependence of the scalar provides a natural matching to cosmology. Scalar-Gauss-Bonnet is particularly rigid and such a scenario does not help. An extra operator makes the theory behave like the other models and the cosmological horizon can be accommodated. The hair, however, is drastically altered.
Conclusions
According to this article, static black holes in general relativity modified by a linear scalar coupling to the Gauss-Bonnet invariant always have hair. However, the presence of this hair makes it incompatible with a cosmological horizon. On the other hand, scalar-tensor models with time-dependent scalar fields can easily match with cosmology. Scalar-Gauss-Bonnet models do not have this advantage and require an additional operator to behave like other models and accommodate a cosmological horizon. However, this modification drastically alters the hair of the black holes.
Future Roadmap
Challenges
- Cosmological Horizon Compatibility: The main challenge in moving forward with the scalar-Gauss-Bonnet model is finding a way to make it compatible with a cosmological horizon. This requires introducing an additional operator or modifying the existing framework, which can be a complicated task.
- Altered Hair: The modification required to accommodate a cosmological horizon in the scalar-Gauss-Bonnet model drastically alters the hair of black holes. Understanding the implications and effects of this altered hair is an important challenge for further research.
Opportunities
- Other Scalar-Tensor Models: The article suggests that other scalar-tensor models with time-dependent scalars naturally match with cosmology. Exploring these models further and comparing them with the scalar-Gauss-Bonnet model could provide valuable insights and potential alternatives.
- Natural Matching to Cosmology: The opportunity to understand and utilize the natural matching between scalar-tensor models and cosmology opens up new avenues for studying the evolution of black holes and the universe at large.
Roadmap
- Further investigate the compatibility of the scalar-Gauss-Bonnet model with a cosmological horizon, possibly by exploring the introduction of an additional operator or modification to the existing framework.
- Analyze the effects and implications of the altered hair in the scalar-Gauss-Bonnet model, understanding its influence on black hole properties and dynamics.
- Conduct a comparative study between the scalar-Gauss-Bonnet model and other scalar-tensor models with time-dependent scalars to determine the advantages and disadvantages of each in terms of cosmology compatibility and black hole hair.
- Investigate the natural matching between scalar-tensor models and cosmology to gain a deeper understanding of the evolution of black holes and the universe.
Note: The future roadmap outlined above is based on the conclusions and implications presented in the article. Further research and analysis may be required to fully understand the challenges and opportunities on the horizon in this field.
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