玻色-爱因斯坦凝聚体广义相对论星
Bose-Einstein Condensate general relativistic stars
摘要：
我们分析的可能性，由于它们的超流体性质，一些紧凑的天体可能包含一个显着的一部分，他们的物质在一个玻色-爱因斯坦凝聚体的形式。为了研究凝聚体，我们使用具有任意非线性的Gross-Pitaevskii方程。通过引入波函数的马德隆表示，我们根据连续性方程和流体动力学欧拉方程来表达系统的动力学。非相对论性和牛顿性的玻色-爱因斯坦引力凝聚体可以被描述为气体，其密度和压力由正压状态方程关联。在四次非线性凝聚体的情况下，状态方程是指数为1的多方方程。在牛顿引力凝聚体的近似下，用Lane-Emden方程描述了引力凝聚体的结构，并给出了该方程的精确解。本文还讨论了旋转凝聚体的情况。用非相对论和相对论状态方程数值研究了具有四次非线性的广义相对论组态，确定了稳定组态的最大质量。粒子质量约为2个中子质量（库珀对），散射长度约为10-20 μ m的凝聚体，其最大质量约为2 M太阳，最大中心密度约为0.1-0.3 × 10^16 g/cm ^3，最小半径在10-20 km范围内。这样，我们得到了一大类稳定的天体，其基本天体物理参数（质量和半径）敏感地依赖于凝聚粒子的质量，并在散射长度。我们还提出，最近观测到的质量在2-2.4 M太阳的中子星是玻色-爱因斯坦凝聚体星。
英文摘要：
We analyze the possibility that due to their superfluid properties some compact astrophysical objects may contain a significant part of their matter in the form of a Bose-Einstein condensate. To study the condensate we use the Gross-Pitaevskii equation, with arbitrary non-linearity. By introducing the Madelung representation of the wave function, we formulate the dynamics of the system in terms of the continuity equation and of the hydrodynamic Euler equations. The non-relativistic and Newtonian Bose-Einstein gravitational condensate can be described as a gas, whose density and pressure are related by a barotropic equation of state. In the case of a condensate with quartic non-linearity, the equation of state is polytropic with index one. In the framework of the Thomas-Fermi approximation the structure of the Newtonian gravitational condensate is described by the Lane-Emden equation, which can be exactly solved. The case of the rotating condensate is also discussed. General relativistic configurations with quartic non-linearity are studied numerically with both non-relativistic and relativistic equations of state, and the maximum mass of the stable configuration is determined. Condensates with particle masses of the order of two neutron masses (Cooper pair) and scattering length of the order of 10-20 fm have maximum masses of the order of 2 M_sun, maximum central density of the order of 0.1-0.3 10^16 g/cm^3 and minimum radii in the range of 10-20 km. In this way we obtain a large class of stable astrophysical objects, whose basic astrophysical parameters (mass and radius) sensitively depend on the mass of the condensed particle, and on the scattering length. We also propose that the recently observed neutron stars with masses in the range of 2-2.4 M_sun are Bose-Einstein Condensate stars.
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