Gravitational Wu-Yang Monopoles

Abstract

We show that in an asymptotically flat space where an S-Matrix can be defined, dual supertranslations leave all its matrix elements invariant and the Hilbert space of asymptotic states factorizes into distinct super-selection sectors, labeled by their dual supertranslation charges. These results suggest that dual supertranslation may be interpreted as a redundant gauge symmetry of asymptotically flat spacetimes. This would allow to recast general relativity as a theory of diffeomorphisms possessing an additional asymptotic gauge symmetry. We then use the conjectured dual supertranslation gauge symmetry to construct a gravitational equivalent of the Wu-Yang monopole solution. The metric describing the solution is defined using two overlapping patches on the celestial sphere. The solution is regular on each one of the patches separately and differentiable in the overlap region, where the two descriptions are identical by virtue of a dual supertranslation gauge transformation. Our construction provides an alternative to Misner's interpretation of the Taub-NUT metric. In particular, we find that using our approach the Taub-NUT metric can be made regular everywhere on the celestial sphere and at the same time it is devoid of closed timelike curves, provided that the bound $\frac{m}{\ell }\le \sqrt{\frac{5}{27}}$ on the ratio of mass to NUT charge is obeyed.

25 pages

References in corpus (12)

• On BMS Invariance of Gravitational Scattering
• BMS supertranslations and Weinberg's soft graviton theorem
• The classical double copy for Taub-NUT spacetime
• The Double Copy of Electric-Magnetic Duality
• New dual gravitational charges
• Monopoles, shockwaves and the classical double copy
• Tower of subleading dual BMS charges
• Properties of Dual Supertranslation Charges in Asymptotically Flat Spacetimes
• Asymptotic Dynamics in Perturbative Quantum Gravity and BMS Supertranslations
• Magnetic Soft Charges, Dual Supertranslations and 't Hooft Line Dressings
• Taub-NUT from the Dirac monopole
• Taming Dirac strings and timelike loops in vacuum gravity

Cited by in corpus (12)

• The Double Copy of Electric-Magnetic Duality
• Topology and Wilson lines: global aspects of the double copy
• Classical double copy at null infinity
• Topological Terms and the Misner String Entropy
• The Precession Caused by Gravitational Waves
• Gravitational Dyonic Amplitude at One-Loop and its Inconsistency with the Classical Impulse
• Duality and four-dimensional black holes: gravitational waves, algebraically special solutions, pole skipping, and the spectral duality relation in holographic thermal CFTs
• Charges in the Extended BMS Algebra: Definitions and Applications
• Scattering Amplitudes for Monopoles: Pairwise Little Group and Pairwise Helicity
• Dual Komar Mass, Torsion and Riemann-Cartan Manifolds
• The Radial Action from Probe Amplitudes to All Orders
• Dualized Gravity beyond Linear Approximation