We investigate the tachyonic instability of Kerr-Newman (KN) black hole with
a rotation parameter $a$ in the Einstein-Chern-Simons-scalar theory coupled
with a quadratic massive scalar field. This instability analysis corresponds to
exploring the onset of spontaneous scalarization for KN black holes. First, we
find no $a$-bound for $alpha<0$ case by considering (1+1)-dimensional
analytical method. A direct numerical method is adopted to explore
(2+1)-dimensional time evolution of a massive scalar perturbation with positive
and negative $alpha$ to obtain threshold curves numerically. We obtain
threshold curves $alpha_{rm th}(a)$ of tachyonic instability for positive
$alpha$ without any $a$-bounds. We expect to find the same threshold curves
$alpha_{rm th}(a)$ of tachyonic instability for negative $alpha$ without any
$a$-bound because its linearized scalar theory is invariant under the
transformation of $alphato -alpha $ and $thetato -theta$. In addition, it
is found that the scalar mass term suppresses tachyonic instability of KN black
holes.
According to the article, the authors investigate the tachyonic instability of Kerr-Newman (KN) black holes with a rotation parameter a in the Einstein-Chern-Simons-scalar theory coupled with a quadratic massive scalar field. The purpose of this analysis is to explore the onset of spontaneous scalarization for KN black holes. The following conclusions can be drawn:
1. No a-bound for α<0 case
The authors use a (1+1)-dimensional analytical method and find that there is no bound on the rotation parameter a for the case where α is negative.
2. Numerical exploration of (2+1)-dimensional time evolution
The authors adopt a direct numerical method to explore the time evolution of a massive scalar perturbation with positive and negative α in a (2+1)-dimensional setup. They obtain threshold curves numerically, indicating the values of α that lead to tachyonic instability. They find that there are no a-bounds for positive α.
3. Invariance under transformation of α and θ
The authors expect that the same threshold curves of tachyonic instability (αth(a)) for negative α can be obtained without any a-bound. This is because the linearized scalar theory is invariant under the transformation of α→-α and θ→-θ.
4. Suppression of tachyonic instability by scalar mass term
The authors observe that the presence of a scalar mass term suppresses the tachyonic instability of KN black holes.
Roadmap:
- Further exploration of the tachyonic instability and onset of spontaneous scalarization for KN black holes
- Investigation of the behavior of tachyonic instability with negative α, expected to be similar to the positive α case
- Confirmation of the absence of a-bound for negative α
- Study of the effects of varying the rotation parameter a on tachyonic instability
- Analyze the impact of the scalar mass term on the stability and properties of KN black holes
- Potential applications of the findings in astrophysics and gravitational wave research
Challenges and opportunities:
- Obtaining more precise numerical results to confirm the absence of a-bound for negative α
- Exploring the physical implications and consequences of tachyonic instability and spontaneous scalarization for KN black holes
- Potential for developing new theoretical frameworks or models to explain the observed phenomena
- Possibility of testing the predictions and conclusions through observational data and experiments
Note: The information provided in this article is based on the conclusions drawn by the authors. Further research and peer review may be necessary to validate and expand upon these findings.
Read the original article