Stability of relativistic stars with scalar hairs

Ryotaro Kase; Rampei Kimura; Seiga Sato; Shinji Tsujikawa

doi:10.1103/PhysRevD.102.084037

paper

Stability of relativistic stars with scalar hairs

arXiv:2007.09864 · doi:10.1103/PhysRevD.102.084037

Abstract

We study the stability of relativistic stars in scalar-tensor theories with a nonminimal coupling of the form $F (ϕ) R$ , where $F$ depends on a scalar field $ϕ$ and $R$ is the Ricci scalar. On a spherically symmetric and static background, we incorporate a perfect fluid minimally coupled to gravity as a form of the Schutz-Sorkin action. The odd-parity perturbation for the multipoles $l \geq 2$ is ghost-free under the condition $F (ϕ) > 0$ , with the speed of gravity equivalent to that of light. For even-parity perturbations with $l \geq 2$ , there are three propagating degrees of freedom arising from the perfect-fluid, scalar-field, and gravity sectors. For $l = 0, 1$ , the dynamical degrees of freedom reduce to two modes. We derive no-ghost conditions and the propagation speeds of these perturbations and apply them to concrete theories of hairy relativistic stars with $F (ϕ) > 0$ . As long as the perfect fluid satisfies a weak energy condition with a positive propagation speed squared $c_{m}^{2}$ , there are neither ghost nor Laplacian instabilities for theories of spontaneous scalarization and Brans-Dicke (BD) theories with a BD parameter $ω_{BD} > - 3/2$ (including $f (R)$ gravity). In these theories, provided $0 < c_{m}^{2} \leq 1$ , we show that all the propagation speeds of even-parity perturbations are sub-luminal inside the star, while the speeds of gravity outside the star are equivalent to that of light.

arXiv comment24 pages, 2 figures

Stability of relativistic stars with scalar hairs

Abstract

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