标题： 爱因斯坦场方程的一个正则内部解 显示英文标题

标题： A regular interior solution of Einstein field equations

摘要： 从包含各向同性流体的静态和球对称时空中的爱因斯坦场方程的解出发，我们构建了一个模型来表示具有紧凑率$u=\frac{GM}{c^2R}<0.23577$的致密天体的内部。通过施加径向和切向压力的各向同性条件，这为时间$g_{tt}$和径向$g_{rr}$度规势生成了一个二阶常微分方程，该方程可以针对特定的$g_{tt}$函数求解。该解的图形分析表明它是物理上可接受的，也就是说，密度、压力和声速都是正的、规则的且单调递减的函数，此外，由于满足绝热指数的标准，该解是稳定的。 当采用质量$M=1.44^{+0.15}_{-0.14}M_\odot$和半径$R=13.02^{+1.24}_{-1.06}km$的数据，这些数据对应于脉冲星 PSR J0030+045 的估计值，我们得到最大致密性$u=0.19628$的中心密度$\rho_c=7.5125\times 10^{17} kg/m^3$和最小致密性$u=0.13460$的$\rho_c= 2.8411 \times 10^{17} kg/m^3$，这些与这类恒星预期的值一致。 显示英文摘要

摘要： Starting from the solution of the Einstein field equations in a static and spherically symmetric spacetime which contains an isotropic fluid, we construct a model to represent the interior of compact objects with compactness rate $u=\frac{GM}{c^2R}<0.23577$. The solution is obtained by imposing the isotropy condition for the radial and tangential pressures, this generates an ordinary differential equation of second order for the temporal $g_{tt}$ and radial $g_{rr}$ metric potentials, which can be solved for a specific function of $g_{tt}$. The graphic analysis of the solution shows that it is physically acceptable, that is to say, the density, pressure and speed of sound are positive, regular and monotonically decreasing functions, also, the solution is stable due to meeting the criteria of the adiabatic index. When taking the data of mass $M=1.44^{+0.15}_{-0.14}M_\odot$ and radius $R=13.02^{+1.24}_{-1.06}km$ which corresponds to the estimations of the star PSR J0030+045 we obtain values of central density $\rho_c=7.5125\times 10^{17} kg/m^3$ for the maximum compactness $u=0.19628$ and of $\rho_c= 2.8411 \times 10^{17} kg/m^3$ for the minimum compactness $u=0.13460$, which are consistent with those expected for this type of stars.