论文标题
用标态头发的相对论恒星的稳定性
Stability of relativistic stars with scalar hairs
论文作者
论文摘要
我们研究了相对论恒星在标量调整理论中的稳定性，其形式$ f（ϕ）r $的非微小耦合，其中$ f $取决于标量field $ ϕ $和$ r $是RICCI量表。在球形对称和静态背景下，我们结合了一种完美的流体，最小化与重力耦合为Schutz-Sorkin动作的形式。在条件$ f（ϕ）> 0 $的情况下，多孔的奇数扰动$ l \ geq 2 $，重力速度等于光的速度。对于$ l \ geq 2 $的偶数扰动，由完美的流体，标量场和重力部门产生了三个传播的自由度。对于$ l = 0，1 $，动态自由度降低至两种模式。我们得出了这些扰动的无孔条件和传播速度，并将其应用于具有$ f（ϕ）> 0 $的毛茸茸的相对论恒星的具体理论。只要完美的液体以较弱的能量状况满足较弱的能量状况，正式的繁殖速度$ c_m^2 $，对于自发标量的理论和brans-dicke（BD）理论既没有幽灵也没有laplacian的不稳定性，而BD参数$ω_{\ rm bd}> - rm bd}> -3/2 $（包括$ fitity $ f（包括$ f）。在这些理论中，提供了$ 0 <c_m^2 \ le 1 $，我们表明，偶数扰动的所有传播速度都是恒星内部的亚亮度，而恒星外部的重力速度则相当于光。
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.
