The null-surface formulation (NSF) of general relativity differs markedly from the conventional approach. The conventional approach to general relativity is concerned with local fields such as the metric, whereas the NSF focuses on surfaces. The NSF has two distinct but mathematically equivalent interpretations: (a) Future-directed light rays leave a spacetime point and intersect future null-infinity. The resulting surface, known as a light-cone cut, encodes the properties of the spacetime; (b) The angular coordinates (Bondi coordinates) of null-infinity are used to label past light cones, thereby producing a family of null surfaces. These will satisfy the NSF field equations and a solution of these equations provides a description of spacetime. This paper features a new exact solution that, for the first time, directly links the two interpretations, thereby illustrating both approaches and demonstrating their equivalence. The solution and its properties are first explored in 2+1 dimensions, after which, the generalization to 3+1 is outlined.

广义相对论的零面公式（NSF）与传统方法明显不同。广义相对论的传统方法关注的是局部场，例如度量，而 NSF 则关注表面。 NSF 有两种不同但在数学上等效的解释：（a）未来定向光线离开时空点并与未来零无穷远相交。由此产生的表面（称为光锥切割）编码了时空的属性； (b) 零无穷大的角坐标（邦迪坐标）用于标记过去的光锥，从而产生一系列零表面。这些将满足 NSF 场方程，并且这些方程的解提供了时空的描述。本文提出了一种新的精确解决方案，首次将两种解释直接联系起来，从而说明了这两种方法并证明了它们的等价性。首先在 2+1 维度中探索该解决方案及其属性，然后概述对 3+1 的推广。