Gravitationally induced zero modes of the Faddeev-Popov operator in the Coulomb gauge for Abelian gauge theories

Understand

It is shown that on curved backgrounds, the Coulomb gauge Faddeev-Popov operator can have zero modes even in the abelian case.

• These zero modes cannot be eliminated by restricting the path integral over a certain region in the space of gauge potentials.
• The conditions for the existence of these zero modes are studied for static spherically symmetric spacetimes in arbitrary dimensions.
• For this class of metrics, the general analytic expression of the metric components in terms of the zero modes is constructed.