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The non-spherical ground state of Proca stars

C. A. R. Herdeiro, E. Radu, N. Sanchis-Gual, N. M. Santos, E. dos Santos Costa Filho

Abstract

Spherical Proca Stars (PSs) are regarded as the ground state amongst the family of PSs. In accordance, spherical PSs are thought to have a fundamental branch of stable solutions. In this Letter, we provide energetic, morphological and dynamical evidence that spherical PSs are actually excited states. The ground state is shown to be a family of static, non-spherical, in fact prolate, PSs. The spherical stars in the fundamental branch, albeit stable against spherical perturbations, turn out to succumb to non-spherical dynamics, undergoing an isometry breaking into prolate PSs. We also provide evidence for the dynamical formation of prolate PSs, starting from spherical dilute initial data, via gravitational cooling. Consequently, PSs provide a remarkable example of (possibly compact) relativistic stars, in General Relativity minimally coupled to a simple, physical, field theory model, where staticity plus stability implies non-sphericity.

The non-spherical ground state of Proca stars

Abstract

Spherical Proca Stars (PSs) are regarded as the ground state amongst the family of PSs. In accordance, spherical PSs are thought to have a fundamental branch of stable solutions. In this Letter, we provide energetic, morphological and dynamical evidence that spherical PSs are actually excited states. The ground state is shown to be a family of static, non-spherical, in fact prolate, PSs. The spherical stars in the fundamental branch, albeit stable against spherical perturbations, turn out to succumb to non-spherical dynamics, undergoing an isometry breaking into prolate PSs. We also provide evidence for the dynamical formation of prolate PSs, starting from spherical dilute initial data, via gravitational cooling. Consequently, PSs provide a remarkable example of (possibly compact) relativistic stars, in General Relativity minimally coupled to a simple, physical, field theory model, where staticity plus stability implies non-sphericity.
Paper Structure (4 equations, 4 figures, 1 table)

This paper contains 4 equations, 4 figures, 1 table.

Figures (4)

  • Figure 1: Domain of existence of monopolar (spherical, $\ell=0$), dipolar ($\ell=1$) and quadrupolar ($\ell=2$) scalar boson stars (left panel) and PSs (right panel) in $M$$vs.$$\omega$ diagrams. The morphology of surfaces of constant Komar energy density is also provided. We have selected 12 illustrative solutions in the Proca case, detailed in Table I, for the dynamical studies below.
  • Figure 2: Prolate/spherical (main panel/inset) PSs do not have/have nodes. Both illustrative solutions have $\omega/\mu=0.9$.
  • Figure 3: Frequency squared $\Omega^2$ for spherical perturbations of monopolar ($\ell=0$) scalar (top) and Proca (bottom) stars. Dashed (solid) lines are stable (unstable) stars.
  • Figure 4: Snapshots in the $x$-$z$ plane of the imaginary part of the Proca scalar potential di2018dynamical (green panels) and energy density (blue panels) in PS evolutions. (Two leftmost columns) Solution 3, illustrating the stability of prolate PSs. (Three central columns) Solution 7, illustrating the isometry breaking of spherical PSs into prolate stars, accompanied by a kick. (Three rightmost columns) Formation scenario, illustrating the formation of a prolate star from an initial dilute spherical Proca cloud.