AI 中文总结
研究通过有限距离类光超曲面的卡罗尔几何来探究类光无穷远之外的引力记忆，利用罗宾逊 - 特劳特曼时空构建准局部卡罗尔耗散系统，明确其与邦迪规范关系，揭示有限屏幕记忆与邦迪记忆联系及相关修正，还得到一些副产品成果。
AI 中文摘要
我们通过研究具有卡罗尔几何的有限距离类光超曲面来研究类光无穷远之外的引力记忆。我们表明，有限类光屏的内禀简并几何、光学数据和类光布朗 - 约克张量定义了一个准局部卡罗尔耗散系统，为表征辐射通过后的残余几何响应提供了自然框架。为使此构造明确并与标准渐近描述比较，我们使用罗宾逊 - 特劳特曼时空作为精确可解的辐射背景。对于渐近平坦的罗宾逊 - 特劳特曼几何，我们将解转换到邦迪规范并直接根据罗宾逊 - 特劳特曼场提取渐近数据。在线性化部分，邦迪剪切纯粹是电的，并产生与向最终史瓦西几何弛豫相关的标准位移记忆效应。我们表明，有限屏幕记忆的主导大半径无迹分量简化为邦迪位移记忆，而有限距离修正保留了额外的聚焦、嵌入依赖性、角漂移、库仑数据和近区信息。因此，邦迪记忆作为更广泛的准局部卡罗尔响应的通用渐近投影出现。接近最终史瓦西视界的晚期屏幕呈现指数衰减的非各向同性卡罗尔数据，仅留下各向同性类光布朗 - 约克应力。作为副产品，我们构建了具有非零宇宙学常数的二阶辐射振幅的罗宾逊 - 特劳特曼解，并使用全息字典研究相关的能量通量，发现所得电荷不遵循通用单调性性质。
英文摘要
We investigate gravitational memory beyond null infinity by studying finite-distance null hypersurfaces endowed with Carrollian geometry. We show that the intrinsic degenerate geometry, optical data, and null Brown--York tensor of a finite null screen define a quasilocal Carrollian dissipative system, providing a natural framework to characterize the residual geometric response after the passage of radiation. To make this construction explicit and compare it with the standard asymptotic description, we use Robinson--Trautman spacetimes as an exactly solvable radiative setting. For asymptotically flat Robinson--Trautman geometries, we transform the solution to Bondi gauge and extract the asymptotic data directly in terms of the Robinson--Trautman field. In the linearized sector, the Bondi shear is purely electric and produces the standard displacement-memory effect associated with the relaxation toward the final Schwarzschild geometry. We show that the leading large-radius tracefree component of the finite-screen memory reduces to the Bondi displacement memory, while finite-distance corrections retain additional focusing, embedding dependence, angular drift, Coulombic data, and near-zone information. Thus, Bondi memory emerges as the universal asymptotic projection of a broader quasilocal Carrollian response. Late-time screens approaching the final Schwarzschild horizon exhibit exponentially decaying non-isotropic Carrollian data, leaving only the isotropic null Brown--York stress. As a by-product, we construct the Robinson--Trautman solution with nonzero cosmological constant to second order in the radiative amplitude and use the holographic dictionary to study the associated energy fluxes and find that the resulting charge does not obey a universal monotonicity property.
Comments78 pages, 3 figures
