Abstract
We connect two different approaches for calculating functional determinants on quotients of hyperbolic spacetime: the heat kernel method and the quasinormal mode method. For the example of a rotating BTZ background, we show how the image sum in the heat kernel method builds up the logarithms in the quasinormal mode method, while the thermal sum in the quasinormal mode method builds up the integrand of the heat kernel. More formally, we demonstrate how the heat kernel and quasinormal mode methods are linked via the Selberg zeta function. We show that a 1-loop partition function computed using the heat kernel method may be cast as a Selberg zeta function whose zeros encode quasinormal modes. We discuss how our work may be used to predict quasinormal modes on more complicated spacetimes.
Highlights
Functional determinants of kinetic operators are of interest in theoretical physics because they allow for the study of quantum effects
As we observed for a real scalar field on the rotating BTZ black hole background in (59), when we tune the effective conformal dimensions ∆2mi0 to the zeros of the Selberg zeta function, we find that the quasinormal modes ω∗ associated with the higher spin field in question First are identified with the thermal (Matsubara) we show again how ∆imi
We have demonstrated the relationship between the heat kernel and quasinormal mode methods for calculating 1-loop determinants, both directly and formally
Summary
Functional determinants of kinetic operators are of interest in theoretical physics because they allow for the study of quantum effects. The differential equation (3) can be solved For quotients of such spacetimes, such as thermal AdS and the BTZ black hole, the method of images allows us to calculate the complete heat kernel. The relationship between quasinormal modes and the Patterson-Selberg zeta function was presented in [20,21] We build on these previous works constructing a connection between the heat kernel and quasinormal methods. After reviewing the heat kernel and quasinormal mode methods for computing 1-loop partition functions, in Section 2 we explicitly connect the heat kernel and quasinormal mode expressions for both scalar fields and gravitons in the 2+1 dimensional rotating BTZ black hole background.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
