Hair formation in the background of noncommutative reflecting stars

Abstract

We investigate scalar condensations around noncommutative compact reflecting stars. We find that the neutral noncommutative reflecting star cannot support the existence of scalar field hairs.In the charged noncommutative reflecting star spacetime, we provide upper bounds for star radii.Above the bound, scalar fields cannot exist outside the star. In contrast, when the star radius is below the bound, we show that the scalar field can condense. We also obtain the largest radii of scalar hairy reflecting stars.

No hair theorem for spherically symmetric regular compact stars with Dirichlet boundary conditions

“…We should point out that this property is very different from cases in black holes, where black hole no hair theorem holds for any size of the horizon [35,36]. Similar to the charged shell case, it was found that large horizonless reflecting stars tend to have no scalar field hair [37][38][39][40][41][42]. Moreover, large horizonless stars with Neumann boundary conditions also cannot support the static scalar field hair [43,44].…”

Large regular reflecting stars have no scalar field hair

“…In the charged horizonless reflecting shell spacetime, it was analytically found that the static scalar field cannot exist outside the shell when the shell radius is large enough [25][26][27]. Moreover, it was shown that charged horizonless reflecting stars cannot support the existence of the scalar field when the star radius is above an upper bound [28][29][30][31][32]. And the no scalar hair behavior also appears in the large size regular star with other surface boundary conditions [33,34].…”

No scalar hair theorem for neutral Neumann stars: Static massive scalar fields nonminimally coupled to gravity

“…In fact, it was shown that static scalar fields cannot condense outside charged reflecting shells of large radii [34][35][36]. Large charged reflecting stars also cannot support static scalar field hairs [37][38][39][40][41][42][43][44]. Moreover, it was found that scalar fields cannot exist outside compact stars with Neumann surface boundary conditions [45,46].…”