论文标题
tolman-oppenheimer-volkoff方程的单数解决方案的分类定理和属性
Classification theorem and properties of singular solutions to the Tolman-Oppenheimer-Volkoff equation
论文作者
论文摘要
Tolman-Oppenheimer-Volkoff（TOV）方程除了常规解决方案外，还可以接受单数溶液。在这里，我们证明了以下定理。对于（i）是从熵函数获得的任何方程式，（ii）具有正压，并且（iii）满足主要的能量条件，可以将TOV方程从内部到中心的边界集成。因此，EOS的热力学一致性排除了病理溶液，其中积分在有限的半径上终止（由于水平或能量密度的差异 /零）。在中心，质量函数要么消失（常规溶液），要么是负（单数解）。对于单数溶液，中心的度量是局部同构至负质量施瓦茨柴尔兹柴尔兹时空的同构。这意味着物质是稳定的，因为奇异性是强烈的排斥性。我们表明，奇异的解决方案的行为表现良好：它们是有限的加速器，并且它们与具有边界的全球双曲线时空相吻合。最后，我们展示了如何修改状态的非物理方程以获得非病理解决方案，并且我们对奇异溶液的动力稳定性进行了初步研究。
The Tolman-Oppenheimer-Volkoff (TOV) equation admits singular solutions in addition to regular ones. Here, we prove the following theorem. For any equation of state that (i) is obtained from an entropy function, (ii) has positive pressure and (iii) satisfies the dominant energy condition, the TOV equation can be integrated from a boundary inwards to the center. Hence, thermodynamic consistency of the EoS precludes pathological solutions, in which the integration terminates at finite radius (because of horizons, or divergences / zeroes of energy density). At the center, the mass function either vanishes (regular solutions) or it is negative (singular solutions). For singular solutions, the metric at the center is locally isomorphic to negative-mass Schwarzschild spacetime. This means that matter is stabilized because the singularity is strongly repulsive. We show that singular solutions are causally well behaved: they are bounded-acceleration complete, and they are conformal to a globally hyperbolic spacetime with boundary. Finally, we show how to modify unphysical equations of state in order to obtain non-pathological solutions, and we undertake a preliminary investigation of dynamical stability for singular solutions.
