Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions

Abstract

We consider a real, massive scalar field in BTZ spacetime, a 2+1-dimensional black hole solution of the Einstein's field equations with a negative cosmological constant. First, we analyze the space of classical solutions in a mode decomposition and we characterize the collection of all admissible boundary conditions of Robin type which can be imposed at infinity. Secondly, we investigate whether, for a given boundary condition, there exists a ground state by constructing explicitly its two-point function. We demonstrate that for a subclass of the boundary conditions it is possible to construct a ground state that locally satisfies the Hadamard property. In all other cases, we show that bound state mode solutions exist and, therefore, such construction is not possible.

17 pages, 3 figures

References in corpus (5)

• Pragmatic mode-sum regularization method for semiclassical black-hole spacetimes
• Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions
• Stationary scalar clouds around a BTZ black hole
• Black Hole Vacua and Rotation
• Renormalized vacuum polarization on rotating warped AdS3 black holes

Cited by in corpus (4)

• Superradiance in the BTZ black hole with Robin boundary conditions
• Ground and thermal states for the Klein-Gordon field on a massless hyperbolic black hole with applications to the anti-Hawking effect
• Vacuum polarization on three-dimensional anti-de Sitter space-time with Robin boundary conditions
• Hidden freedom in the mode expansion on static spacetimes