Quantum Effects Of BTZ Black Hole

BTZ black hole is a kind of special?2+1?-dimension black hole,whose metric can be obtained by solving?2+1?-dimension Einstein-Maxwell equations with negative cosmological constant.BTZ black hole has special spacetime structure and relatively concise metric,so it is a very suitable candidate which can be used to study the properties of black holes.In this theory,we mainly investigate the absorption and radiation of charged BTZ black hole in nonminimally coupled scalar field and AdS/CFT correspondence in noncommutative BTZ black hole background.This will reveal the quantum properties of BTZ black holes at the Planck scale.In Chapter 2,we set up the Klein-Gorden equation for the charged BTZ black hole in nonminimally coupled scalar field and study its reflection coefficient,absorp-tion cross section and decay rate.We find:?)The reflection coefficient is directly governed by Hawking temperature,scalar wave frequency,Bekenstein–Hawking entropy,angular momentum8)and coupling constant.?)The reflection coefficient monotonically decreases as the scalar wave fre-quencyincreases and eventually tends to zero in the high energy regime,when the coupling constant is?0.25.However,when the coupling constant is=0.17?conformal value?,the reflection coefficient will decrease firstly and then tend to a finite constant in the high energy regime.Furthermore,we find that the finite constant is affected by parameter.The largercorresponds to a smaller finite constant.?)The absorption cross section monotonically decreases from a finite constant and eventually tends to zero as the wave frequencyincreases.In the case8)=0,the absorption cross section does not necessarily coincide with the area of the horizon.The value of the dimensionless parameter₍(6?7?8???0?/increases as the parametersandincrease.??The decay rate monotonically decreases asincreases and eventually tends to zero in the high energy regime.In Chapter 3,we firstly revise the analytical expressions for various spin QNM in noncommutative BTZ background.We use the QNM to explore the AdS/CFT correspondence and quantization of area/entropy,and we find:The exact agreement in BTZ background is also corrected in noncommutative BTZ background.At the Planck scale,the noncommutativity of this black hole modifies the Hawking temper-atures and QNM frequencies,but it doesn't affect the conformal weights??,??.Due to the existence of the noncommutativity,the area/entropy spectrum is not equidistant any more.