Black holes with quantum corrections in $3d$: The case of Page curve in Lindblad, greybody factor, and Lyapunov exponent

Abstract

In this work, first we discuss black holes with quantum corrections as an open quantum system and apply Lindblad formalism to explain the ``zig-zag" behavior in the Hawking- Page curve and radiation process, specially by considering the effects of exceptional points. Then, we calculate quantum corrections for various parameters of $3d$ Cotler-Jensen theory which is ${\text{AdS}}_3$ with reparametrized modes. At each step of the calculations, we compare the results with the case of JT. We then calculate quantum-corrected greybody factor for various black hole solutions, and specially for the case of Cotler-Jensen theory. Finally, we study the effects of quantum corrections on Lyapunov exponent, potential, and quantum information structure of black holes.

64 pages, 21 figures