We study the system of static scalar fields coupled to charged compact reflecting stars through both analytical and numerical methods. We enclose the star in a box and our solutions are related to ...cases without box boundaries when putting the box far away from the star. We provide bottom and upper bounds for the radius of the scalar hairy compact reflecting star. We obtain numerical scalar hairy star solutions satisfying boundary conditions and find that the radius of the hairy star in a box is continuous in a range, which is very different from cases without box boundaries where the radius is discrete in the range. We also examine effects of the star charge and mass on the largest radius.
We analyze condensation behaviors of neutral scalar fields outside horizonless reflecting stars in the Einstein-Maxwell-scalar gravity. It was known that minimally coupled neutral scalar fields ...cannot exist outside horizonless reflecting stars. In this work, we consider non-minimal couplings between scalar fields and Maxwell fields, which is included to aim to trigger formations of scalar hairs. We analytically demonstrate that there is no hair theorem for small coupling parameters below a bound. For large coupling parameters above the bound, we numerically obtain regular scalar hairy configurations supported by horizonless reflecting stars.
A
bstract
We study the system constructed by charged scalar fields linearly coupled to asymptotically flat horizonless compact reflecting stars. We obtain bounds on the charge of the scalar field, ...below which the scalar hairy star is expected to suffer from nonlinear instabilities. It means that scalar hairy regular configurations are unstable for scalar fields of small charge. For the highly-charged star, there are also bounds on radii of regular compact reflecting stars. When the star radius is below the bound, the hairy star is always unstable.
We study condensation behaviors of static scalar fields in the regular asymptotically AdS reflecting star spacetime. With analytical methods, we provide upper bounds for the radii of the scalar hairy ...reflecting stars. Above the bound, there is no scalar hair theorem for the star. Below the bound, we numerically obtain charged scalar hairy reflecting star solutions and in particular, the radii of the hairy stars are discrete, which is similar to known results in other reflecting object backgrounds. For every set of parameters, we search for the largest AdS hairy star radius, study effects of parameters on the largest hairy star radius and also find difference between properties in this AdS reflecting star background and those in the flat reflecting star spacetime. Moreover, we show that scalar fields cannot condense around regular AdS reflecting stars when the star charge is small or the cosmological constant is negative enough.
The existence of null circular geodesics in the background of non-extremal spherically symmetric asymptotically flat black holes has been proved in previous works. An interesting question that ...remains, however, is whether extremal black holes possess null circular geodesics outside horizons. In the present paper, we focus on the extremal spherically symmetric asymptotically flat hairy black holes. We show the existence of the fastest circular trajectory around an extremal black hole. As the fastest trajectory corresponds to the position of null circular geodesics, we prove that null circular geodesics exist outside extremal spherically symmetric asymptotically flat hairy black holes.
In a very interesting paper, Hod has proven that the equatorial null circular geodesic provides the extreme orbital period to circle a kerr black hole, which is closely related to the Fermat's ...principle. In the present paper, we extend the discussion to kerr black holes with scalar field hair. We show that the circle with the extreme orbital period is still identical to the null circular geodesic. Our analysis also implies that the Hod's theorem may be a general property in any axially symmetric spacetime with reflection symmetry on the equatorial plane.
We study static massive scalar field condensations in the regular asymptotically flat reflecting star background. We impose Neumann reflecting surface boundary conditions for the scalar field. We ...show that the no hair theorem holds in the neutral reflecting star background. For charged reflecting stars, we provide bounds for radii of hairy reflecting stars. Below the lower bound, there is no regular compact reflecting star and a black hole will form. Above the upper bound, the scalar field cannot condense around the reflecting star or no hair theorems exist. And in between the bounds, we obtain scalar configurations supported by Neumann reflecting stars.
For massless scalar fields, a relation Δn=32π for n→∞ was observed in the scalar-Gauss-Bonnet theory. In the present paper, we extend the discussion by including a nonzero scalar field mass. For ...massive scalar fields, we show that the relation Δn=32π for n→∞ still holds. We demonstrate this relation with both analytical and numerical methods. The analytical analysis implies that this relation may be a very universal behavior.
We study hair mass distributions in noncommutative Einstein-Born-Infeld hairy black holes with non-zero cosmological constants. We find that the larger noncommutative parameter makes the hair easier ...to condense in the near horizon area. We also show that Hod's lower bound can be evaded in the noncommutative gravity. However, for large black holes with a non-negative cosmological constant, Hod's lower hair mass bound almost holds in the sense that nearly half of the hair lays above the photonsphere.
We study the existence of scalar fields outside neutral reflecting shells. We consider static massive scalar fields non-minimally coupled to the Gauss–Bonnet invariant. We analytically investigated ...properties of scalar fields through the scalar field equation. In the small scalar field mass regime, we derive a compact resonance formula for the allowed masses of scalar fields in the composed scalar field and shell configurations.
PDF
