论文标题
天空不变：Schwarzschild Spacetime的新形式不变
The sky invariant: A new conformal invariant for Schwarzschild spacetime
论文作者
论文摘要
引入了一类新的与给定时空$ m $的共形不变式，以利用任何光线$γ$的保形几何形状。通过给定点$ p $的光线的每一个一致性都定义了该点的天空$ s（p）$。新的保形不变式是在时空$ m $的天空中定义的，被称为天空不变。在浅射线上定义的自然保形协变量衍生物及其相关的协变量使我们显示出存在天然的保形不变差分的存在，该弧线加上限制了保形的协变量衍生物的曲率，可用于构建一个被称为天空曲率的天空。可以在任何符号操作软件系统上实现的算法，以计算天空曲率，并在Schwarzschild SpaceTime中说明了天空曲率的主要思想和明确计算。
A new class of conformal invariants for a given spacetime $M$ is introduced exploiting the conformal geometry of any light ray $Γ$. Each congruence of light rays passing through a given point $p$ defines the sky $S(p)$ of such point. The new conformal invariants are defined on the bundle of skies of the spacetime $M$, being called sky invariants accordingly. The natural conformal covariant derivative defined on a light ray and its associated covariant calculus allows us show the existence of a natural conformal invariant differential of arc that, together with the restriction of the curvature of the conformal covariant derivative, can be used to construct a sky invariant that will be called the sky curvature. An algorithm, that can be implemented on any symbolic manipulation software system, to compute the sky curvature will be discussed and the main ideas and the explicit computation of the sky curvature are illustrated in Schwarzschild spacetime.
