渐近平坦引力宇称条件的放宽
Relaxing the Parity Conditions of Asymptotically Flat Gravity
摘要：
四维空间无穷远渐近平坦时空是由第一性原理定义的，没有对Weyl张量施加宇称条件或限制。证明了Einstein-Hilbert作用量在补充一个反常反项时是一个正确的变分原理，该反项打破了渐近平移、超平移和对数平移不变性.庞加莱变换以及超平移和对数平移都与代表渐近对称群的有限和守恒电荷有关。洛仑兹电荷和对数平移在调节器的变化下发生了剧烈的变化。洛仑兹电荷一般是渐近场的非线性泛函，但当宇称条件成立时，它可以简化为众所周知的线性表达式。我们还定义了一个协变相空间的渐近平坦的时空的宇称条件，但没有限制的外尔张量。在这个相空间中，反常在经典意义上不起动力学作用。超平移是纯规范，渐近对称群是期望的庞加莱群。
英文摘要：
Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counter-term which breaks asymptotic translation, supertranslation and logarithmic translation invariance. Poincaré transformations as well as supertranslations and logarithmic translations are associated with finite and conserved charges which represent the asymptotic symmetry group. Lorentz charges as well as logarithmic translations transform anomalously under a change of regulator. Lorentz charges are generally non-linear functionals of the asymptotic fields but reduce to well-known linear expressions when parity conditions hold. We also define a covariant phase space of asymptotically flat spacetimes with parity conditions but without restrictions on the Weyl tensor. In this phase space, the anomaly plays classically no dynamical role. Supertranslations are pure gauge and the asymptotic symmetry group is the expected Poincaré group.
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