Abstract
On an $n$-dimensional, massless, topological black hole with hyperbolic sections, we construct the two-point function both of a ground state and of a thermal state for a real, massive, free scalar field arbitrarily coupled to scalar curvature and endowed with Robin boundary conditions at conformal infinity. These states are used to compute the response of an Unruh-DeWitt detector coupled to them for an infinite proper time interval along static trajectories. As an application, we focus on the massless conformally coupled case and we show, numerically, that the anti-Hawking effect, which is manifest on the three-dimensional case, does not occur if we consider a four-dimensional massless hyperbolic black hole. On the one hand, we argue that this result is compatible with what happens in the three- and four dimensional Minkowski spacetime, while, on the other hand, we stress that it generalizes existing results concerning the anti-Hawking effect on black hole spacetimes.
Highlights
We investigate the behavior of an Unruh-DeWitt detector following static trajectories and interacting, for an infinite proper time interval, either with a ground state or with a Kubo-Martin-Schwinger (KMS) state of a real, massive scalar field on a massless hyperbolic black hole
VI, as an application of the framework established, we perform a numerical analysis for the massless conformally coupled, real scalar field and we study the dependence of the transition rate on the energy gap, on the boundary condition, on the spacetime dimension and on the local Hawking temperature
We have written down an explicit expression for the transition rate of an Unruh-DeWitt detector following static trajectories and interacting, for an infinite proper time interval, with the physical states constructed
Summary
We investigate the behavior of an Unruh-DeWitt detector following static trajectories and interacting, for an infinite proper time interval, either with a ground state or with a Kubo-Martin-Schwinger (KMS) state of a real, massive scalar field on a massless hyperbolic black hole. Observe that one can consider more general boundary conditions, e.g., [19], we shall not discuss them further in this work For these reasons, we shall be considering a generic real, massive scalar field on a massless hyperbolic black hole with arbitrary Robin boundary conditions and, as a first step we investigate how to construct the two-point function of a ground and of a thermal state.
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