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Register a new userDynamical evolution of electromagnetic perturbation in the background of a scalar hairy black hole in Horndeski theory
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We have investigated dynamical evolution of electromagnetic perturbation in a scalar hairy black hole spacetime, which belongs to solutions in Horndeski theory with a logarithmic cubic term. Our results show that the parameter $alpha$ affects the existence of event horizon and modifies the asymptotical structure of spacetime at spatial infinity, which imprints on the quasinormal frequency of electromagnetic perturbation. Moreover, we find that the late-time tail of electromagnetic perturbation in this background depends also on the parameter $alpha$ due to the existence of solid angle deficit. The presence of the parameter $alpha$ makes the perturbation field decay more rapidly. These imply that the spacetime properties arising from the logarithmic cubic term in the action play important roles in the dynamical evolutions of the electromagnetic perturbation in the background of a scalar hairy black hole.
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Using Leavers continue fraction and time domain method, we study the wave dynamics of phantom scalar perturbation in a Schwarzschild black string spacetime. We find that the quasinormal modes contain the imprint from the wavenumber $k$ of the fifth dimension. The late-time behaviors are dominated by the difference between the wavenumber $k$ and the mass $mu$ of the phantom scalar perturbation. For $k<mu$, the phantom scalar perturbation in the late-time evolution grows with an exponential rate as in the four-dimensional Schwarzschild black hole spacetime. While, for $k=mu$, the late-time behavior has the same form as that of the massless scalar field perturbation in the background of a black hole. Furthermore, for $k>mu$, the late-time evolution of phantom scalar perturbation is dominated by a decaying tail with an oscillation which is consistent with that of the usual massive scalar field. Thus, the Schwarzschild black string is unstable only against the phantom scalar perturbations which satisfy the wavelength $lambda>2pi/mu$. These information can help us know more about the wave dynamics of phantom scalar perturbation and the properties of black string.
We present an exact static black hole solution of Einstein field equations in the framework of Horndeski Theory by imposing spherical symmetry and choosing the coupling constants in the Lagrangian so that the only singularity in the solution is at $r=0$. The analytical extension is built in two particular domains of the parametric space. In the first domain we obtain a solution exhibiting an event horizon analogous to that of the Schwarzschild geometry. For the second domain, we show that the metric displays an exterior event horizon and a Cauchy horizon which encloses a singularity. For both branches we obtain the corresponding Hawking temperature which, when compared to that of the Schwarzschild black hole, acquires a correction proportional to a combination of the coupling constants. Such a correction also modifies the definition of the entropy of the black hole.
We study the dynamical evolution of a massless scalar perturbation in the Hov{r}ava-Lifshitz black-hole spacetimes with the coupling constants $lambda={1/3}$, $lambda={1/2}$ and $lambda=3$, respectively. Our calculation shows that, for the three cases, the scalar perturbations decay without any oscillation in which the decay rate imprints the parameter of the Hov{r}ava-Lifshitz black hole. The results are quite different from those in the Schwarzschild AdS black hole and can help us understand more about the Hov{r}ava-Lifshitz gravity.
Using Leavers continue fraction and time domain method, we investigate the wave dynamics of phantom scalar perturbation in the background of Schwarzschild black hole. We find that the presence of the negative kinetic energy terms modifies the standard results in quasinormal spectrums and late-time behaviors of the scalar perturbations. The phantom scalar perturbation in the late-time evolution will grow with an exponential rate.
We study certain bi-scalar-tensor theories emanating from conformal symmetry requirements of Horndeskis four-dimensional action. The former scalar is a Galileon with shift symmetry whereas the latter scalar is adjusted to have a higher order conformal coupling. Employing technics from local Weyl geometry certain Galileon higher order terms are thus constructed to be conformally invariant. The combined shift and partial conformal symmetry of the action, allow us to construct exact black hole solutions. The black holes initially found are of planar horizon geometry embedded in anti de Sitter space and can accommodate electric charge. The conformally coupled scalar comes with an additional independent charge and it is well-defined on the horizon whereas additional regularity of the Galileon field is achieved allowing for time dependence. Guided by our results in adS space-time we then consider a higher order version of the BBMB action and construct asymptotically flat, regular, hairy black holes. The addition of the Galileon field is seen to cure the BBMB scalar horizon singularity while allowing for the presence of primary scalar hair seen as an independent integration constant along-side the mass of the black hole.
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