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.

arXiv comment9 pages, 1 figure

References in corpus (42)

• Holographic Superconductors
• Kerr black holes with scalar hair
• Shadows of Kerr black holes with scalar hair
• Black hole hair in generalized scalar-tensor gravity
• Dressing a black hole with a time-dependent Galileon
• Kerr black holes with Proca hair
• Stationary Scalar Clouds Around Rotating Black Holes
• Kerr-Newman scalar clouds
• Explosion and final state of an unstable Reissner-Nordstrom black hole
• Stationary resonances of rapidly-rotating Kerr black holes
• Kerr-Newman black holes with stationary charged scalar clouds
• Hairy Black Holes and Null Circular Geodesics
• Black holes have no short hair
• Non-linear Q-clouds around Kerr black holes
• Stability of black holes in Einstein-charged scalar field theory in a cavity
• Black hole solutions in Einstein-charged scalar field theory
• Stationary scalar configurations around extremal charged black holes
• The large-mass limit of cloudy black holes
• The superradiant instability regime of the spinning Kerr black hole
• Inside black holes with synchronized hair
• No-scalar-hair theorem for spherically symmetric reflecting stars
• Scalar field configurations supported by charged compact reflecting stars in a curved spacetime
• Charged massive scalar field configurations supported by a spherically symmetric charged reflecting shell
• No-hair theorems for a static and stationary reflecting star
• On the thermodynamics of the black hole and hairy black hole transitions in the asymptotically flat spacetime with a box
• Synchronous frequencies of extremal Kerr black holes: resonances, scattering and stability
• Charged reflecting stars supporting charged massive scalar field configurations
• Marginally bound resonances of charged massive scalar fields in the background of a charged reflecting shell
• No nonminimally coupled massless scalar hair for spherically symmetric neutral reflecting stars
• On instabilities of scalar hairy regular compact reflecting stars
• Static scalar field condensation in regular asymptotically AdS reflecting star backgrounds
• Skyrmions, Skyrme stars and black holes with Skyrme hair in five spacetime dimension
• The extreme orbital period in scalar hairy kerr black holes
• Hair mass bound in the black hole with nonzero cosmological constants
• Phases of Global AdS Black Holes
• Scalar field condensation behaviors around reflecting shells in Anti-de Sitter spacetimes
• Hair distributions in noncommutative Einstein-Born-Infeld black holes
• Scalar condensation behaviors around regular Neuman reflecting stars
• Hair formation in the background of noncommutative reflecting stars
• A general holographic insulator/superconductor model away from the probe limit
• Spinning boson stars and hairy black holes with non-minimal coupling
• No scalar hair theorem for neutral Neumann stars: static massive scalar fields nonminimally coupled to gravity

Cited by in corpus (8)

• Revisiting compact star in $F(R)$ gravity: Roles of chameleon potential and energy conditions
• No hair theorem for massless scalar fields outside asymptotically flat horizonless reflecting compact stars
• No hair theorem for bound-state massless static scalar fields outside horizonless Neumann compact stars
• No scalar hair theorem for neutral Neumann stars: static massive scalar fields nonminimally coupled to gravity
• No-go theorem for static boson stars with negative cosmological constants
• 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
• Regular scalar field around reflecting stars and black holes, and reflecting star polarization