Physical significance of generalized boundary conditions: An Unruh-DeWitt detector viewpoint on PAdS2×S2

On PAdS2×S2, we construct the two-point correlation functions for the ground and thermal states of a real Klein-Gordon field admitting generalized (γ,v)-boundary conditions. We follow the prescription recently outlined in [1] for two different choices of secondary solutions. For each of them, we obtain a family of admissible boundary conditions parametrized by γ∈[0,π2]. We study how they affect the response of a static Unruh-DeWitt detector. The latter not only perceives variations of γ, but also distinguishes between the two families of secondary solutions in a qualitatively different, and rather bizarre, fashion. Our results highlight once more the existence of a freedom in choosing boundary conditions at a timelike boundary which is often neglected, though it has a notable associated physical significance.