论文标题
定期满足弱和强能条件的KERR溶液的内部解决方案
Regular Interior Solutions to the Solution of Kerr which Satisfy the Weak and the Strong Energy Conditions
论文作者
论文摘要
如果两个函数$ f（r）$和$ h（r）$匹配的一类解决方案的线元素与KERR的解决方案相匹配，那么它依赖于满足某些匹配条件的条件。 Ricci张量$ r_ {μν} $的非消失组件，Ricci scalar $ r $，第二阶曲率不变$ k $，ricci张量的特征值，能量密度$ $ $ $，切线压力$ p _ p_ p_ p_ p_ p_ p_ p _ $计算。给出了$ f（r）$的功能，$ r $和$ k $，因此解决方案是常规的。功能$ h（r）$应该使其提供的解决方案至少满足弱能量条件（WEC）。明确给出了几美元（R）$，为此提供了$ $ $ $ $ $，$ p _ {\ perp} $和$μ+P _ {\ perp} $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $的图表的明确给出。结果表明，类的所有解决方案都是各向异性流体溶液，并且同类中没有完美的流体溶液。
The line element of a class of solutions which match to the solution of Kerr on an oblate spheroid if the two functions $ F(r)$ and $H(r)$ on which it depends satisfy certain matching conditions is presented. The non vanishing components of the Ricci tensor $R_{μν}$, the Ricci scalar $ R$, the second order curvature invariant $K$, the eigenvalues of the Ricci tensor, the energy density $μ$, the tangential pressure $P_{\perp}$, and the quantity $μ+P_{\perp}$ are calculated. A function $F(r)$ is given for which $R$ and $K$ and therefore the solutions are regular. The function $ H(r) $ should be such that the solution it gives satisfies at least the Weak Energy Conditions (WEC). Several $H(r)$ are given explicitly for which the resulting solutions satisfy the WEC and also the Strong Energy Conditions (SEC) and the graphs of their $μ$, $P_{\perp}$ and $μ+P_{\perp}$ for certain values of their parameters are presented. It is shown that all solutions of the class are anisotropic fluid solutions and that there are no perfect fluid solutions in the class.
