论文标题
使用黑色字符串集来表示紧凑型恒星 -
Representation of compact stars using the black string set--up
论文作者
论文摘要
这项工作致力于使用黑色字符串框架来表示$ 4D $球形对称和静态紧凑型恒星配置为$ 5D $时空。 我们编写四个和五个维线元素以及四个和五个维能动量张量，以使四维和五个维数与函数$ a（z）$相关，其中$ z $代表额外的维度。值得注意的是，我们选择的线元素所选形式的结果是，对于能量动量张量和$ a（z）$的结果，即$ 5D $方程将减少到运动的四个维度方程的通常形式。同样，五维保护方程式采用了四个维度保护方程的形式。值得一提的是，尽管我们的方法很简单，但这种减少形式可以用来将其他四维对象的其他类型代表到未来作品中的额外尺寸。此外，在我们的假设下，沿额外尺寸的压力的符号由四维能量动量张量的痕迹给出。 此外，我们对功能的简单选举$ a（z）$修改了引起的4维紧凑型恒星配置的某些功能，例如质量 - 摩擦关系，惯性的动量，热力学变量的核心价值，仅举几例。此外，该模型的拓扑为$ {s}^{2} \ times {s}^{1} $，而不是5-维结构的$ {s}^{3} $拓扑。
This work is devoted to provide a way of representing $4D$ spherically symmetric and static compact stellar configurations into a $5D$ space time, using the black string framework. We write the four and five dimensional line elements and the four and five dimensional energy momentum tensor such that the four and five dimensional quantities are related by a function $A(z)$, where $z$ represents to the extra dimension. Remarkably, one consequence of our chosen form for the line element, for the energy momentum tensor and for $A(z)$, is the fact that the $5D$ equations are reduced to the usual form of the four dimensional equations of motion. Also, the five dimensional conservation equation adopts the form of the four dimensional conservation equation. It is worth mentioning that, although our methodology is simple, this form of reduction could serve to represent other types of four dimensional objects into an extra dimension in future works. Furthermore, under our assumptions the sign of the pressure along the extra dimension is given by the trace of the four dimensional energy momentum tensor. Furthermore, our simple election for the function $A(z)$ modifies some features of the induced 4--dimensional compact stellar configuration, such as the mass--radius relation, the momentum of inertia, the central values of the thermodynamic variables, to name a few. Besides, the topology of this model is ${S}^{2}\times {S}^{1}$ and not the ${S}^{3}$ topology of the 5--dimensional structures.
