1-Loop Partition Functions and Schwinger Pair Production in a Near-Horizon Near-Extremal Black Hole Background

In this thesis, we study 1-loop partition functions and Schwinger pair production in a two-dimensional Anti-de Sitter ( ) space-time, that arises in the near-horizon near-extremal limit of a Reissner-Nordstrӧm black hole in four space-time dimensions.

This study is motivated by the recently renewed interest in Jackiw-Teitelboim (JT) gravity in two dimensions, arising from the dimensional reduction on a two-sphere of an Einstein-Maxwell theory in four space-time dimensions, and which serves as a toy model for understanding quantum gravity and black hole physics.

In this context, we analyse the classical trajectories of a scalar particle in an black hole space-time in the presence of a constant external electric field. We discuss the symmetries of the point-particle Lagrangian and we subsequently quantize the particle system. Employing the heat kernel method and character zeta function techniques developed recently in the literature, we derive the regularized 1-loop effective action for a charged particle in .Using this effective action, we determine the Schwinger pair production rate in the black hole background when the electric field strength surpasses a critical threshold.

Our findings demonstrate that the Schwinger pair production rate in an black hole space-time equals those obtained in other coordinate systems, such as in Poincaré patch coordinates and in global coordinates. This agreement is non-trivial due to the fact that these coordinate systems are related by transformations involving the time-like coordinate, resulting in different Hamiltonians.

Additionally, in agreement with previous studies, we find that the regularized 1-loop effective action has a logarithmic term that depends on the scale factor, reminiscent of the logarithmic area correction to the Bekenstein-Hawking entropy of an extremal Reissner-Nordstrӧm black hole in four space-time dimensions.

In our work that we submitted to JHEP, we demonstrated that this logarithmic term corresponds to a boundary entanglement entropy calculation in the dual , which is identifed as a de Alfaro-Fubini-Furlan conformal quantum mechanics model at coupling . This computation is performed via a thermofield double state in the dual . We take this correspondence to be a realization of the Ryu-Takayanagi conjecture in