We revisit the question of whether classical general relativity obeys, beyond the linearised order, an analogue of the global U(1) electric-magnetic duality of Maxwell theory, with the Riemann tensor playing the role analogous to the field strength. Following contradictory claims in the literature, we present a simple gauge-invariant argument that the duality does not hold. The duality condition is the conservation of the helicity charge. Scattering amplitudes of gravitons in general relativity, and of gluons in Yang-Mills theory, violate this selection rule already at tree level. Indeed, the maximally-helicity-violating (MHV) amplitudes are famous for their simplicity. The duality in the linearised theories is, therefore, broken by the interactions. In contrast, the tree-level scattering amplitudes in duality-invariant theories of non-linear electromagnetism are known to obey helicity conservation. While the duality is not a symmetry of the full theory of general relativity, it does hold within a sector of the solution space, including vacuum type D solutions, where the duality is known to rotate between mass and NUT charge.

我们重新审视经典广义相对论是否超越线性化顺序，服从麦克斯韦理论的全局 U(1) 电磁对偶性的模拟，黎曼张量扮演类似于场强的角色。根据文献中相互矛盾的主张，我们提出了一个简单的规范不变论证，即对偶性不成立。对偶条件是螺旋电荷守恒。广义相对论中引力子的散射振幅和杨米尔斯理论中胶子的散射振幅，在树级别就已经违反了这一选择规则。事实上，最大螺旋性破坏（MHV）振幅因其简单性而闻名。因此，线性化理论中的二元性被相互作用打破了。相比之下，非线性电磁学的对偶不变理论中的树级散射幅度已知遵守螺旋性守恒。虽然对偶性不是整个广义相对论的对称性，但它确实在解空间的某个扇区内成立，包括真空 D 型解，其中已知对偶性在质量和 NUT 电荷之间旋转。