有压力的准黑洞：相对论性带电球体作为冰冻恒星
Quasiblack holes with pressure: relativistic charged spheres as the frozen stars
摘要：
在广义相对论中，当引力势$W^2$和电势场$ϕ$服从$W^{2}= a\left(-ε\, ϕ+ b\right)^2 +c$形式的关系时，其中$a$、$b$和$c$是任意常数，而$ε=\pm1$（光速$c$和牛顿常数$G$归为一），一类非常有趣的带压带电系统出现了。我们把$W$和$ϕ$之间的上述关系称为Weyl-Guilfoyle关系，它推广了通常的Weyl关系，其中$a=1$。对于外尔关系和外尔-吉尔弗约尔关系，带电流体，如果存在的话，可以具有非零压力。遵循Weyl-Guilfoyle关系的流体称为Weyl-Guilfoyle流体。这些流体，在球对称的假设下，表现出的解可以与电真空Reissner-Nordström时空相匹配，产生全局渐近平坦的冷带电恒星。我们证明了Guilfoyle发现的一类特殊的球对称恒星有一个行为良好的极限，对应于一个极端的Reissner-Nordström准黑洞，即，其中准视界内的流体具有电荷和压力，而准视界外的几何由极值Reissner-Nordström度规给出。分析了这类带电恒星和类黑洞的主要物理性质。这些恒星和准黑洞提供的一个重要发展是，没有压力的解决方案，Majumdar-Papapetrou解决方案，是不稳定的动力学扰动。有压力的解决方案可以避免这种不稳定性。如果是稳定的，这些有压力的冷准黑洞，这些致密的相对论性带电球体，其实是冰冻的恒星。
英文摘要：
In general relativity coupled to Maxwell's electromagnetism and charged matter, when the gravitational potential $W^2$ and the electric potential field $ϕ$ obey a relation of the form $W^{2}= a\left(-ε\, ϕ+ b\right)^2 +c$, where $a$, $b$ and $c$ are arbitrary constants, and $ε=\pm1$ (the speed of light $c$ and Newton's constant $G$ are put to one), a class of very interesting electrically charged systems with pressure arises. We call the relation above between $W$ and $ϕ$, the Weyl-Guilfoyle relation, and it generalizes the usual Weyl relation, for which $a=1$. For both, Weyl and Weyl-Guilfoyle relations, the electrically charged fluid, if present, may have nonzero pressure. Fluids obeying the Weyl-Guilfoyle relation are called Weyl-Guilfoyle fluids. These fluids, under the assumption of spherical symmetry, exhibit solutions which can be matched to the electrovacuum Reissner-Nordström spacetime to yield global asymptotically flat cold charged stars. We show that a particular spherically symmetric class of stars found by Guilfoyle has a well-behaved limit which corresponds to an extremal Reissner-Nordström quasiblack hole with pressure, i.e., in which the fluid inside the quasihorizon has electric charge and pressure, and the geometry outside the quasihorizon is given by the extremal Reissner-Nordström metric. The main physical properties of such charged stars and quasiblack holes with pressure are analyzed. An important development provided by these stars and quasiblack holes is that without pressure the solutions, Majumdar-Papapetrou solutions, are unstable to kinetic perturbations. Solutions with pressure may avoid this instability. If stable, these cold quasiblack holes with pressure, i.e., these compact relativistic charged spheres, are really frozen stars.
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