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

TL;DR

This paper studies the ground state of a massive scalar field in BTZ spacetime with Robin boundary conditions, analyzing classical solutions, boundary conditions, and the existence of Hadamard states.

Contribution

It characterizes all admissible Robin boundary conditions in BTZ spacetime and constructs ground states for a subclass of these conditions, highlighting when such states exist.

Findings

Ground states exist for certain Robin boundary conditions.

Bound state solutions prevent ground state construction in other cases.

Constructed ground states satisfy the Hadamard property locally.

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.