On the Membrane Paradigm and Spontaneous Breaking of Horizon BMS Symmetries

Understand

We consider a BMS-type symmetry action on isolated horizons in asymptotically flat spacetimes.

• From the viewpoint of the non-relativistic field theory on a horizon membrane, supertranslations shift the field theory spatial momentum.
• The latter is related by a Ward identity to the particle number symmetry current and is spontaneously broken.
• The corresponding Goldstone boson shifts the horizon angular momentum and can be detected quantum mechanically.