Location
MC 6460
Candidate
Maria Rosa Preciado Rivas| Applied Mathematics, University of Waterloo
Title
Unruh-DeWitt Detectors Freely Falling into BTZ Black Holes
Abstract
Understanding what an observer experiences while falling into a black hole is part of the larger problem of describing quantum phenomena in strong gravitational fields, for which no complete and generally accepted theory of quantum gravity yet exists. Even within quantum field theory in curved spacetime, the question is nontrivial because particle content is observer-dependent: what a detector registers depends on its trajectory, the state of the field, and the spacetime geometry. This calculation is particularly challenging for an infalling observer, whose trajectory is nonstationary and not adapted to the black hole's symmetries.
This thesis asks what an infalling observer registers using Unruh-DeWitt detectors coupled to a quantum scalar field. We study detectors in the static and rotating Bañados-Teitelboim-Zanelli (BTZ) black holes and the RP2 geon. These spacetimes are locally anti-de Sitter in three dimensions (AdS3) and are constructed as quotients of AdS3. This construction allows us to obtain their field correlation functions from the AdS3 correlation function using the method of images, making the detector response relatively easy to calculate.
Motivated by conflicting conclusions about whether an infalling detector exhibits a special feature across the horizon in Schwarzschild spacetime, we first study a detector falling into a static BTZ black hole. We find that its response remains smooth and monotonic across the event horizon. However, the transition rate, defined as the time derivative of the response function, exhibits points of nondifferentiability that we call glitches. We discuss the geometric origin of these glitches and how they are related to the global topology of the spacetime.
Extending the calculation to the rotating BTZ black hole and the RP2 geon, we find that the locations and symmetries of the glitches are sensitive to both the rotational and hidden topology of the spacetime. Both modifications of the static BTZ spacetime introduce new families of glitches and produce qualitatively different behavior in the transition rate.
Finally, motivated by previous work in Schwarzschild spacetime, we define an effective temperature by comparing the infalling response to that of a geodesic detector in a thermal AdS3 state of known temperature. This effective temperature increases smoothly during infall, remains finite at the event horizon, and is nearly independent of the detector gap over the range studied. Our results extend the effective temperature prescription to a different black hole geometry, showing that the principal qualitative features found in Schwarzschild black holes persist in BTZ black holes.
This thesis provides a partial answer to the guiding question of what an observer perceives while falling into a black hole, using Unruh-DeWitt detectors: an infalling detector need not register a special feature at the event horizon; still, its transition rate can reveal the global structure of the spacetime, and its transition function allows for the estimation of an effective temperature.