论文标题
渐近剪切和无侵占的固有保形几何形状
Asymptotic Shear and the Intrinsic Conformal Geometry of Null-Infinity
论文作者
论文摘要
在本文中，我们提出了渐近平面时间辐射相空间的新几何化：我们表明，通过引力波的存在诱导的几何形状可以理解为对拖拉机的概括，以概括为改编成对调节中等融合度的曲线。因此，整个形式主义是通过建筑明显不变的。我们首先表明，渐近剪切的选择等于在零含量的尺度上的订单二的线性差分操作员的选择。我们将这些运营商称为庞加莱运营商。然后，我们证明庞加莱运营商与特定类别的拖拉机连接是一对一的对应关系，我们称之为“无正常”（它们概括了共形几何形状的正常拖拉机连接）。拖拉机曲率编码引力波的存在以及平坦的无效拖拉机连接的非唯一性对应于文献中已广泛讨论的“重力真空脱落”。因此，这项工作将重力辐射相空间的研究带入了（cartan）连接和相关束的研究。这特别是允许扩散相空间的不变性。
In this article we propose a new geometrization of the radiative phase space of asymptotically flat space-times: we show that the geometry induced on null-infinity by the presence of gravitational waves can be understood to be a generalisation of the tractor calculus of conformal manifolds adapted to the case of degenerate conformal metrics. It follows that the whole formalism is, by construction, manifestly conformally invariant. We first show that a choice of asymptotic shear amounts to a choice of linear differential operator of order two on the bundle of scales of null-infinity. We refer to these operators as Poincaré operators. We then show that Poincaré operators are in one-to-one correspondence with a particular class of tractor connections which we call "null-normal" (they generalise the normal tractor connection of conformal geometry). The tractor curvature encodes the presence of gravitational waves and the non-uniqueness of flat null-normal tractor connections correspond to the "degeneracy of gravity vacua" that has been extensively discussed in the literature. This work thus brings back the investigation of the radiative phase space of gravity to the study of (Cartan) connections and associated bundles. This should allow, in particular, to proliferate invariants of the phase space.
