Vacua of the gravitational field

Abstract

The Poincaré invariant vacuum is not unique in quantum gravity. The BMS supertranslation symmetry originally defined at null infinity is spontaneously broken and results in inequivalent Poincaré vacua. In this paper we construct the unique vacua which interpolate between past and future null infinity in BMS gauge and which are entirely characterized by an arbitary Goldstone boson defined on the sphere which breaks BMS invariance. We show that these vacua contain a defect which carries no Poincaré charges but which generically carries superrotation charges. We argue that there is a huge degeneracy of vacua with multiple defects. We also present the single defect vacua with its canonically conjugated source which can be constructed from a Liouville boson on the stereographic plane. We show that positivity of the energy forces the stress-tensor of the boson to vanish as a boundary condition. Finite superrotations, which turn on the sources, are therefore physically ruled out as canonical transformations around the vacua. Yet, infinitesimal superrotations are external symplectic symmetries which are associated with conserved charges which characterize the Goldstone boson.

Accepted in JHEP, comments added, 34 pages

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• Black Hole Entropy and Soft Hair
• The Weyl BMS group and Einstein's equations
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• Soft Gravitons & the Memory Effect for Plane Gravitational Waves
• Soft hairy horizons in three spacetime dimensions
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• Anomalies in gravitational charge algebras of null boundaries and black hole entropy
• Black Hole Horizon Fluffs: Near Horizon Soft Hairs as Microstates of Three Dimensional Black Holes
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• Classical static final state of collapse with supertranslation memory
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• Loop-corrected subleading soft theorem and the celestial stress-tensor
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• Berry Phases on Virasoro Orbits
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• Gravitational vacua in the Newman-Penrose formalism
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