论文标题
在较高的尺寸中重力的渐近结构
The Asymptotic Structure of Gravity in Higher Even Dimensions
论文作者
论文摘要
我们研究了较高的尺寸的经典重力中渐近对称性的概念，其中$ d = 6 $时空维度为原型。与四个维度不同，某些非线性持续存在，这需要我们进行完整的非线性分析。我们表明，在将来（过去）无限无穷大的一对对称痕量张力张子中，免费数据被参数化。这涉及辐射场的重新定义。我们定义了一个符号结构，该结构在$ {\ cal i}^{\ pm} $中生成辐射相空间，并具有适当的边界条件，这些条件通过超级翻译的作用保留。我们得出了与超级翻译矢量场相关的电荷，并且该电荷与使用整个非线性理论中运动方程得出的电荷相匹配。我们详细介绍了超级翻译电荷，邦德质量方面和“重力记忆”之间的精确关系，从而提供了超出四个维度的非线性重力中红外三角的第一个例子。
We investigate the notion of asymptotic symmetries in classical gravity in higher even dimensions, with $D = 6$ space-time dimensions as the prototype. Unlike in four dimensions, certain non-linearities persist which necessitates the complete non-linear analysis we undertake. We show that the free data is parametrized by a pair of symmetric trace-free tensors at future (past) null infinity. This involves a redefinition of the radiative field. We define a symplectic structure generating the radiative phase space at ${\cal I}^{\pm}$ with appropriate boundary conditions which are preserved by the action of supertranslations. We derive the charge associated to super-translation vector fields and this charge matches with that derived using the equations of motion in the full non-linear theory. We elaborate on the precise relationship between the super-translation charge, the Bondi mass aspect and the "gravitational memory" in six space-time dimensions, thus providing the first example of an infrared triangle in non-linear gravity beyond four dimensions.
