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

Abstract

We study scalar condensation in the background of asymptotically flat spherically symmetric regular Dirichlet stars. We assume that the scalar field decreases as the star surface is approached. Under these circumstances, we prove a no hair theorem for neutral regular compact stars. We also extend the discussion to charged regular compact stars and find an upper bound for the charged star radius. Above the upper bound, the scalar hair cannot exist. Below the upper bound, we numerically obtain solutions of scalar hairy charged stars.

9 pages, 1 figure

References in corpus (9)

• Kerr-Newman scalar clouds
• Kerr-Newman black holes with stationary charged scalar clouds
• Non-linear Q-clouds around Kerr black holes
• The large-mass limit of cloudy black holes
• Charged massive scalar field configurations supported by a spherically symmetric charged reflecting shell
• Synchronous frequencies of extremal Kerr black holes: resonances, scattering and stability
• No nonminimally coupled massless scalar hair for spherically symmetric neutral reflecting stars
• Skyrmions, Skyrme stars and black holes with Skyrme hair in five spacetime dimension
• The extreme orbital period in scalar hairy kerr black holes

Cited by in corpus (4)

• Revisiting compact star in $F(R)$ gravity: Roles of chameleon potential and energy conditions
• No hair theorem for bound-state massless static scalar fields outside horizonless Neumann compact stars
• No scalar hair in nonminimal derivative coupling model for Neumann and Dirichlet reflecting star
• A no-go theorem for scalar fields with couplings from Ginzburg-Landau models