大质量白矮星结构中的广义相对论效应
General Relativistic effects in the structure of massive white dwarfs
摘要：
本文利用Tolman-Oppenheimer-Schmidoff方程研究了白矮星的结构，并将所得结果与牛顿引力方程的结果进行了比较，以证明广义相对论对这类恒星结构的重要性。在这项工作中，我们认为白矮星内的物质的两个状态方程，经常在文献中发现，即，Sirrasekhar和Salpeter状态方程。我们发现，使用牛顿平衡方程，大质量白矮星（$M>1.3M_{\odot}$）的半径被高估与GR的结果相比。对于质量为$1.415M_{\odot}$的白矮星，GR理论的白矮星半径比牛顿理论的小33%。因此，在这种情况下，对于表面引力，广义相对论和牛顿结果之间的差异约为65%。我们将广义相对论质量-半径图描述为$M/M_{\odot}=R/(a+bR+cR^2+dR^3+kR^4)$，其中$a$、$b$、$c$和$d$是从数值结果的拟合过程中获得的参数，而$k=(2.08\times 10^{-6}R_{\odot})^{-1}$是$R_{\odot}$是以km为单位的太阳半径。最后，我们指出GR在确定任何同时依赖于大质量白矮星的质量和半径的物理量方面起着重要的作用。
英文摘要：
In this work we investigate the structure of white dwarfs using the Tolman-Oppenheimer-Volkoff equations and compare our results with those obtained from Newtonian equations of gravitation in order to put in evidence the importance of General Relativity (GR) for the structure of such stars. We consider in this work for the matter inside white dwarfs two equations of state, frequently found in the literature, namely, the Chandrasekhar and Salpeter equations of state. We find that using Newtonian equilibrium equations, the radii of massive white dwarfs ($M>1.3M_{\odot}$) are overestimated in comparison with GR outcomes. For a mass of $1.415M_{\odot}$ the white dwarf radius predicted by GR is about 33\% smaller than the Newtonian one. Hence, in this case, for the surface gravity the difference between the general relativistic and Newtonian outcomes is about 65\%. We depict the general relativistic mass-radius diagrams as $M/M_{\odot}=R/(a+bR+cR^2+dR^3+kR^4)$, where $a$, $b$, $c$ and $d$ are parameters obtained from a fitting procedure of the numerical results and $k=(2.08\times 10^{-6}R_{\odot})^{-1}$, being $R_{\odot}$ the radius of the Sun in km. Lastly, we point out that GR plays an important role to determine any physical quantity that depends, simultaneously, on the mass and radius of massive white dwarfs.
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