Stability of relativistic stars with scalar hairs
Stability of relativistic stars with scalar hairs
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DOI：
10.1103/physrevd.102.084037
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发表时间：
2020-07
影响因子：
5
通讯作者：
R. Kase;Rampei Kimura;S. Sato;S. Tsujikawa
中科院分区：
文献类型：
--
作者：
R. Kase;Rampei Kimura;S. Sato;S. Tsujikawa
我们研究了标量张量理论中的相对论性恒星的稳定性，其非最小耦合形式为$F（\phi）R$，其中$F$依赖于标量场$\phi$，$R$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的奇宇称微扰在条件F（\phi）>0的情况下是无重影的，引力的速度与光速相等。对于偶宇称扰动与l \geq 2$，有三个传播自由度所产生的完美流体，标量场，和重力部门。当l=0，1时，动力自由度降为两个模态.我们推导出无鬼的条件和这些扰动的传播速度，并将它们应用到具体的理论，毛相对论性恒星与$F（\phi）>0$。只要理想流体满足弱能量条件，传播速度平方为c_m^2 $，则自发标量化理论和BD参数>-3/2$的Brans-Dicke（BD）理论（包括f（R）$引力）既不存在鬼不稳定性，也不存在拉普拉斯不稳定性。在这些理论中，假设0 <c_m^2 \le 1$，我们证明了所有偶宇称微扰的传播速度在星星内部都是亚光速，而在星星外部的引力速度与光速相等。
We study the stability of relativistic stars in scalar-tensor theories with a nonminimal coupling of the form $F(\phi)R$, where $F$ depends on a scalar field $\phi$ 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 $F(\phi)>0$, 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 $F(\phi)>0$. 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 $\omega_{\rm BD}>-3/2$ (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.