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arXiv 2007.09864gr-qcastro-ph.COhep-phhep-th
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具有标量毛的相对论星的稳定性

Stability of relativistic stars with scalar hairs

Ryotaro Kase, Rampei Kimura, Seiga Sato, Shinji Tsujikawa

备注：
24 pages, 2 figures
发表信息：
Phys. Rev. D 102, 084037 (2020)
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摘要：

本文研究了标量张量理论中相对论性恒星的稳定性，其中耦合形式为$F(ϕ)R$，其中$F$依赖于标量场$ϕ$，$R$是Ricci标量。在球对称和静态的背景下，我们将一个完美的流体最低限度地耦合到重力作为一种形式的Schutz-Sorkin行动。多极子$l \geq 2$的奇宇称微扰在重力速度与光速相等的条件$F(ϕ)>0$下是无重影的。对于具有$l \geq 2$的偶宇称扰动，有三个传播自由度，分别来自于理想流体、标量场和重力扇区。对于$l=0, 1$，动力学自由度减少到两个模式。我们推导出无鬼的条件和这些扰动的传播速度，并将其应用到具体的理论与$F(ϕ)>0$的毛相对论性恒星。只要理想流体满足传播速度平方为正的弱能量条件，自发标量化理论和具有BD参数$c_m^2$的Brans-Dicke（BD）理论（包括$f(R)$引力）就不会有鬼不稳定性或拉普拉斯不稳定性。在这些理论中，提供了$0<c_m^2 \le 1$，我们表明，所有的传播速度的偶宇称扰动是亚光速的内部的恒星，而外部的重力的速度相当于光。

英文摘要：

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 $ω_{\rm BD}>-3/2$ (including $f(R)$ gravity). In these theories, provided $0<c_m^2 \le 1$, 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.

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