论文标题
用于代表黑色弦风格的常规黑洞的玩具模型
A toy model for representing regular black holes at the black string style
论文作者
论文摘要
我们提供了一种在黑色弦风格中表示四维常规黑洞几何形状的方法。我们阐明约束列表，以使完整的五维几何形状是规则的。遵循这些约束，同时构建了四个维度的几何形状。 用于求解运动方程的假设表明，$ 4D $与$ 5D $ Newton常数之间的关系，这与先前在文献中显示的关系相吻合。此外，运动的$（μ，ν）$组件采用了运动的四个维度方程的形式。同样，五维保护方程式采用了四个维度保护方程的形式。 在起源上，五个维几何形状的拓扑与$ z $ compact的四个维度de-sitter空间和$ s^1 $之间的产品相对应。后者与Kaluza-Klein黑色弦有所不同，其中，拓扑在起点上对应于Schwarzschild Singularity和$ r（s^1）$（$ z $ non compact（compact））之间的产品。完整的五维几何形状的拓扑对应于$ s^2 \ times s^1 $。在径向坐标的无穷大，拓扑对应于Minkowski和$ s^1 $之间的产品。 在诱导的四个维几何形状下，我们以适当的温度和熵值计算热力学的第一定律。
We provide a way of representing a four dimensional regular black hole geometry at the black string style. We enunciate a list of constrains in order to that the complete five dimensional geometry to be regular. Following these constraints were constructed both the four and the five dimensional geometries. The assumptions used to solve the equations of motion suggest a relation between the $4D$ and the $5D$ Newton constants, which coincides with relations previously showed in the literature. Furthermore, the $(μ,ν)$ components of the five dimensional equations of motion adopt the form of the four dimensional equations of motion. Also, the five dimensional conservation equation adopts the form of the four dimensional conservation equation. At the origin the topology of the five dimensional geometry corresponds to the product between the four dimensional de--Sitter space--time and $S^1$ with $z$ compact. This latter differs from the Kaluza-Klein black string, where, at the origin the topology corresponds to the product between the Schwarzschild singularity and $R(S^1)$ for $z$ non compact (compact). The topology of the complete five dimensional geometry corresponds to $S^2 \times S^1$. At the infinity of the radial coordinate the topology corresponds to the product between Minkowski and $S^1$. At the induced four dimensional geometry we compute the first law of thermodynamics with the correct values of temperature and entropy.
