No hair theorem for massless scalar fields outside asymptotically flat horizonless reflecting compact stars

In a recent paper, Hod started a study on no scalar hair theorem for asymptotically flat spherically symmetric neutral horizonless reflecting compact stars. In fact, Hod's approach only rules out massive scalar fields. In the present paper, for massless scalar fields outside neutral horizonless reflecting compact stars, we provide a rigorous mathematical proof on no hair theorem. We show that asymptotically flat spherically symmetric neutral horizonless reflecting compact stars cannot support exterior massless scalar field hairs.Comment: 7 page

Scalar field configurations supported by charged compact reflecting stars in a curved spacetime

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.Comment: 10 pages, 4 figures. Accepted for publication in PLB. arXiv admin note: text overlap with arXiv:1711.0697

Scalar condensation behaviors around regular Neuman reflecting stars

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.Comment: 9 pages, 1 figur

No short hair behaviors of ultra-compact stars

In the black hole spacetime, a no short hair theorem was proved, which states that the effective radius of black hole hairs must extend beyond the null circular orbit. In the present paper, in the horizonless gravity, we find a similar no short hair behavior that the effective radius of matter fields must also extend beyond the null circular orbit of ultra-compact stars.Comment: 6 page

Holographic entanglement entropy in superconductor phase transition with dark matter sector

In this paper, we investigate the holographic phase transition with dark matter sector in the AdS black hole background away from the probe limit. We disclose the properties of phases mostly from the holographic topological entanglement entropy of the system. We find the entanglement entropy is a good probe to the critical temperature and the order of the phase transition in the general model. The behaviors of entanglement entropy at large strip size suggest that the area law still holds with dark matter sector. We also conclude that the holographic topological entanglement entropy is useful in detecting the stability of the phase transitions. Furthermore, we derive the complete diagram of the effects of coupled parameters on the critical temperature through the entanglement entropy and analytical methods.Comment: 15 pages, 7 figure

Studies of a general flat space/boson star transition model in a box through a language similar to holographic superconductors

We study a general flat space/boson star transition model in quasi-local ensemble through approaches familiar from holographic superconductor theories. We manage to find a parameter $\psi_{2}$, which is proved to be useful in disclosing properties of phase transitions. In this work, we explore effects of the scalar mass, scalar charge and St$\ddot{u}$ckelberg mechanism on the critical phase transition points and the order of transitions mainly from behaviors of the parameter $\psi_{2}$. We mention that properties of transitions in quasi-local gravity are strikingly similar to those in holographic superconductor models. We also obtain an analytical relation $\psi_{2}\varpropto(\mu-\mu_{c})^{1/2}$, which also holds for the condensed scalar operator in the holographic insulator/superconductor system in accordance with mean field theories.Comment: 11 pages, 6 figure