具有旋转和空间扭曲的无膨胀动力星的不存在性
Non-existence of expansion-free dynamical stars with rotation and spatial twist
摘要：
扩展以前的工作由相同的作者，我们调查存在的膨胀自由动力星与非零空间扭曲和旋转，并表明，这样的恒星不存在。首先，证明了不存在零扭曲的旋转无膨胀动力星。这是因为这样的恒星不能辐射，它们是无剪切的，在这种情况下，能量密度$ρ$是与时间无关的。其次，我们证明了一个非旋转的膨胀自由的动态星与非零的空间扭曲也不可能存在，因为要么强能量条件必须被违反，即$ρ+3p<0$，或恒星必须是剪切自由，在这种情况下，恒星是静态的（$Θ=Ω=Σ=0$）。最后，如果我们坚持旋转和空间扭曲同时不为零，那么恒星不可能是无剪切的，在这种情况下，我们得到一个二次多项式方程在$ϕ$和$Σ$没有真正的解决方案。这样的恒星不可能存在。
英文摘要：
Extending a previous work by the same authors, we investigate the existence of expansion-free dynamical stars with non-zero spatial twist and rotation and show that such stars cannot exist. Firstly, it is shown that a rotating expansion-free dynamical star with zero twist cannot exist. This is due to the fact that such stars cannot radiate and they are shear-free, in which case the energy density $ρ$ is time independent. Secondly, we prove that a non-rotating expansion-free dynamical star with non-zero spatial twist also cannot exist, as either the strong energy condition must be violated, i.e. $ρ+3p<0$, or the star must be shear-free in which case the star is static ($Θ=Ω=Σ=0$). Finally, if we insist that the rotation and spatial twist are simultaneously non-zero, then the star cannot be shear-free in which case we obtain a quadratic polynomial equation in $ϕ$ and $Σ$ with no real solutions. Therefore such stars cannot exist.
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