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arXiv 2109.06342hep-thgr-qc
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来自对称的引力:对偶性和脉冲波

Gravity from symmetry: Duality and impulsive waves

Laurent Freidel, Daniele Pranzetti

摘要:

我们表明,我们可以推导出的渐近爱因斯坦方程,产生的顺序$1/r$在渐近平坦的重力纯粹从对称性的考虑。这是通过研究Weyl BMS群的作用下的度量和应力-能量张量的泛函的变换性质来实现的,Weyl BMS群是最近引入的渐近对称群,包括2-球面上的度量的任意双同态和局部共形变换。我们的推导,其中包括列入物质来源,导致协变观测值的识别,提供了一个定义的保守电荷参数化的非辐射角相空间。这些观测值,相关的外尔标量,揭示了对偶对称性和自旋2发电机,使我们能够重铸的渐近演化方程在一个简单而优雅的形式作为守恒方程的零流体生活在零无穷大。最后,我们确定非线性引力脉冲波,描述引力真空之间的过渡,是渐近爱因斯坦方程的非微扰解。这为渐近相空间的量子化提供了一个新的图景,其中引力真空是渐近对称群的表示,脉冲波被编码在它们的耦合中。

英文摘要:

We show that we can derive the asymptotic Einstein's equations that arises at order $1/r$ in asymptotically flat gravity purely from symmetry considerations. This is achieved by studying the transformation properties of functionals of the metric and the stress-energy tensor under the action of the Weyl BMS group, a recently introduced asymptotic symmetry group that includes arbitrary diffeomorphisms and local conformal transformations of the metric on the 2-sphere. Our derivation, which encompasses the inclusion of matter sources, leads to the identification of covariant observables that provide a definition of conserved charges parametrizing the non-radiative corner phase space. These observables, related to the Weyl scalars, reveal a duality symmetry and a spin-2 generator which allow us to recast the asymptotic evolution equations in a simple and elegant form as conservation equations for a null fluid living at null infinity. Finally we identify non-linear gravitational impulse waves that describe transitions among gravitational vacua and are non-perturbative solutions of the asymptotic Einstein's equations. This provides a new picture of quantization of the asymptotic phase space, where gravitational vacua are representations of the asymptotic symmetry group and impulsive waves are encoded in their couplings.

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