Quasi-normal Modes Research Of Quantum Black Holes

Quantum gravity theory is the quantization of gravitational field theory,it tries to organically combine the two theoretical pillars of modern physics: General Relativity(GR)and Quantum Mechanics(QM),its establishment will become the most important cornerstone of physics.To this end,physicists have been working to construct a complete theory of quantum gravity,which is not only crucial to understanding the origin and evolution of the universe,but also fundamental to the universality and consistency of quantum theory itself.Loop Quantum Gravity(LQG)is the most popular theory among various unperturbed quantum gravity schemes.It introduces the concept of quantum geometry,points out that gravity is a manifestation of spacetime geometry,and emphasizes the quantum of geometry.Since the theory of loop quantum gravity was put forward,related topics have aroused hot discussion.This paper focuses on quantum black holes using loop quantum gravity to solve the problem of black hole singularity.Loop quantum gravity focuses on the physics of the big Bang singularity and the black hole singularity.In these regions,the curvature of spacetime enters the Planck region,the predictions of general relativity are not reliable and the effects of quantum gravity would take over.Spacetime is no longer smooth and continuous,regions of physical space can be described by a set of interconnected spatial cells.Inspired by loop variables in loop quantum gravity,we approximate the curvature of a connection by introducing polymer parameters and replacing them with exponential versions of variables,analogous to considering a loop that contracts to a point along it.This process,known as polymerization,allows parameters to be kept within the variables of finite polymerization and is widely used in black hole singularities.In this paper,we systematically study the spherically symmetric polymer black hole model recently proposed by Gambini,Olmedo,and Pullin(GOP).In GOP quantum black hole model,a spacelike transition surface replaces the classical singularity.We extended the metric to the white hole region through parameters transformation,studied the geometric structure of GOP quantum black hole,obtained the non-smooth feature of throat,and found the existence of infinite thin shell there.At the same time,we analyzed the main properties of several special positions of the spacetime,and obtained the energy conditions which is consistent with the singularity theorem.To provide reference for possible gravitational wave tests,we also calculate quasi-normal modes in scalar field perturbation,electromagnetic field perturbation,axial gravitational perturbation and Eikonal limit.As expected,the quasi-normal mode frequency of quantum black holes deviates from the classical case,and the quasi-normal mode frequency has the same qualitative trend when taking quantum parameters of different values.We discuss and guess the reason for the occurrence of this quantum correction.