具有流体动力学状态方程的各向异性源正则黑洞
Regular Black Holes from Anisotropic Source with Hydrodynamic Equation of State
AI总结：
研究由各向异性源产生的正则黑洞解，通过假设流体动力学状态方程 $P=P(\ ho)$ 并分解能动张量，得到已知和新的正则黑洞度量，分析声速平方符号变化及亚光速约束对模型参数的限制。
摘要：
我们研究由各向异性能动张量源产生的正则黑洞解。众所周知，球对称正则黑洞内部几何趋近于dS度量。将能动张量分解为各向同性和各向异性分量后，我们假设压力满足流体动力学状态方程 $P= P(\ ho)$，并寻找球对称正则黑洞解。我们考虑不同的 $P(\ ho)$ 形式，这些形式产生了先前已知的正则黑洞解以及各种新度量。我们表明，$P(\ ho)$ 的轮廓在远处趋近于 $0^+$ 时有一个根和一个最大值。因此，扰动声速平方 $c_s^2$ 在 $P$ 达到最大值处改变符号，表明可能存在流体动力学不稳定性。此外，对 $c_s$ 施加亚光速约束对模型参数施加了严格限制，排除了能量密度呈指数衰减的模型。我们建立了强能量条件被违反、$P$ 有根以及 $P$ 达到最大值这三个相对位置之间的普遍层次关系。
英文摘要：
We study regular black hole solutions sourced by an anisotropic energy momentum tensor. It is well known that the geometry of the interior of a spherically symmetric regular black hole approaches the dS metric. Having decomposed the energy momentum tensor into its isotropic and anisotropic components, we assume a hydrodynamic equation of state, $P= P(ρ)$, for the pressure, and look for spherically symmetric, regular black hole solutions. We consider different forms of $ P(ρ)$ which yield the previously known regular black hole solutions, as well as various new metrics. We show that the profile of $ P(ρ)$ has a root and a maximum as it approaches $0^+$ at large distances. Consequently, the square of the sound speed of perturbations, $c_s^2$, changes sign at the point where $P$ reaches its maximum, indicating a potential hydrodynamic instability. In addition, imposing the subluminal bound on $c_s$ puts strong constraints on the model parameters, excluding models in which the energy density has an exponential fall off. We establish a universal hierarchy among the relative positions at which the strong energy condition is violated, at which $P$ has its root, and at which $P$ attains its maximum.
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