论文标题
具有宇宙常数
Stable relativistic polytropic objects with cosmological constant
论文作者
论文摘要
研究了宇宙常数对静态平衡构型的影响和稳定性对相对论多变态球的小径向扰动的稳定性。这项研究通过数值求解静水平衡方程和径向稳定方程，这两者均根据其标准形式进行了修改以引入宇宙常数。对于流体，我们考虑了压力$ p $和一个能量密度$ρ$，通过状态方程$ p =κδ^γ$与$δ=ρ-p/（γ-1）$相连，其中$κ$，$γ$和$γ$和$δ$分别代表了多性变态常数，绝对索引和静止的质量，并分别为流体量。分析了质量，半径和特征频率对宇宙常数和绝热指数的依赖性。对于中央休息质量密度$δ_c$和绝热指数$γ$的范围，我们表明，当宇宙常数$λ> 0 $（$λ<0 $）增加时，星星的质量和半径较大（下）质量和半径较大（下）稳定性（增强）。此外，在一系列具有固定$γ$和$λ$的紧凑型物体中，分别由稳定和不稳定的静态平衡配置构建的区域通过条件$ dm/dΔ_c> 0 $和$ dm/dM/dΔ_c<0 $。
The effects of the cosmological constant on the static equilibrium configurations and stability against small radial perturbations of relativistic polytropic spheres are investigated. This study numerically solves the hydrostatic equilibrium equation and the radial stability equation, both of which are modified from their standard form to introduce the cosmological constant. For the fluid, we consider a pressure $p$ and an energy density $ρ$, which are connected through the equation of state $p=κδ^Γ$ with $δ=ρ-p/(Γ-1)$, where $κ$, $Γ$ and $δ$ represent the polytropic constant, adiabatic index and rest mass density of the fluid, respectively. The dependencies of the mass, radius and eigenfrequency of oscillations on both the cosmological constant and the adiabatic index are analyzed. For ranges of both the central rest mass density $δ_c$ and the adiabatic index $Γ$, we show that the stars have a larger (lower) mass and radius and a diminished (enhanced) stability when the cosmological constant $Λ>0$ ($Λ<0$) is increased (decreased). In addition, in a sequence of compact objects with fixed $Γ$ and $Λ$, the regions constructed by stable and unstable static equilibrium configurations are recognized by the conditions $dM/dδ_c>0$ and $dM/dδ_c<0$, respectively.
