论文标题
充电完美流体星的动态和热力学稳定性
Dynamic and Thermodynamic Stability of Charged Perfect Fluid Stars
论文作者
论文摘要
我们通过将WALD形式主义应用于爱因斯坦 - 麦克斯韦（Einstein-Maxwell）的拉格朗日（Lagrangian）配方，对带电的完美流体恒星的动态和热力学稳定性进行了彻底的分析。结果，我们发现，带电流体的额外电磁场和洛伦兹力的存在都没有任何障碍，这对中性完美流体恒星获得的先前结果的关键步骤都有任何阻碍。因此，我们带电恒星在动态平衡中动态稳定性的标准在与$ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $的能量的非负能量相关的均与及时式杀戮领域相关的无与伦比的非负性的情况下的标准，以验证这些均匀的均匀范围，以验证这些不合格的范围。扰动还意味着动态稳定性与更通用的扰动。另一方面，我们充电恒星在热力学平衡中的热力学稳定性的必要条件是由所有线性的壳上壳扰动的阳性呈阳性，与同等型在Comential of Come-Ensive the the the the the the the the the the the the the the the the the the-timelike杀人率相关的均等的ADM角动量均不变。作为副产品，我们进一步建立了动态和热力学稳定性相对于静态，球体对称的等质电荷恒星的球形对称扰动的等效性。
We perform a thorough analysis of the dynamic and thermodynamic stability for the charged perfect fluid star by applying the Wald formalism to the Lagrangian formulation of Einstein-Maxwell-charged fluid system. As a result, we find that neither the presence of the additional electromagnetic field nor the Lorentz force experienced by the charged fluid makes any obstruction to the key steps towards the previous results obtained for the neutral perfect fluid star. Therefore, the criterion for the dynamic stability of our charged star in dynamic equilibrium within the symplectic complement of the trivial perturbaions with the ADM $3$-momentum unchanged is given by the non-negativity of the canonical energy associated with the timelike Killing field, where it is further shown for both non-axisymmetric and axisymmetric perturbations that the dynamic stability against these restricted perturbations also implies the dynamic stability against more generic perturbations. On the other hand, the necessary condition for the thermodynamic stability of our charged star in thermodynamic equilibrium is given by the positivity of the canonical energy of all the linear on-shell perturbations with the ADM angular momentum unchanged in the comoving frame, which is equivalent to the positivity of the canonical energy associated with the timelike Killing field when restricted onto the axisymmetric perturbations. As a by-product, we further establish the equivalence of the dynamic and thermodynamic stability with respect to the spherically symmetric perturbations of the static, spherically symmetric isentropic charged star.
