Singular excitement beyond the horizon of a rotating black hole

TL;DR

This paper investigates how a Unruh-DeWitt detector's transition rate behaves when freely falling into a rotating BTZ black hole, revealing complex local extremum patterns influenced by black hole rotation and boundary conditions.

Contribution

It extends previous non-rotating BTZ black hole studies by analyzing the effects of rotation on detector transition rates and provides a generalized numerical framework for rotating black holes.

Findings

Transition rates exhibit multiple local extrema near the horizon.

Rotation influences the number and position of extrema.

Results recover non-rotating case as angular momentum approaches zero.

Abstract

Previous studies have shown that an Unruh-DeWitt (UDW) detector, when coupled linearly to a massless scalar field and permitted to fall radially into certain black holes, will exhibit non-monotonicity in its transition properties near the horizon. Specifically, the transition probability of a detector freely falling into a (3+1)-dimensional Schawrzschild black hole, when considering the Unruh and Hartle-Hawking vacuum states, was shown to possess a local extremum at horizon crossing [K.K. Ng et al., New J. Phys. 24 (2022) 103018]. The transition rate of a detector falling into a static (2+1)-dimensional Ba\~nados-Teitelboim-Zanelli (BTZ) black hole, for the Hartle-Hawking state, was also found to have multiple local extrema near the horizon under certain parameter settings [M.R. Preciado-Rivas et al., arXiv:2402.14908v1]. These discoveries are of interest, as they suggest that the event horizon of a black hole may be distinguishable to a local probe when QFT effects are included. In this paper, we explore the problem of a UDW detector falling freely into a rotating BTZ black hole. We numerically compute the detector's transition rate for different values of black hole mass, black hole angular momentum, detector energy gap, and field boundary conditions at infinity. Our results lead to a more generalized description of the behaviour of particle detectors in BTZ black hole spacetime, from which the previous non-rotating BTZ case can be retrieved in the limit as angular momentum vanishes.