【摘要】：本文研究了2維引力與弦模型中黑洞的物理性質(zhì),第一章介紹了2維引力與弦模型的發(fā)展?fàn)顩r和背景知識;第二章分析了Jackiw-Teitelboim模型中場方程的可解性質(zhì),通過引入Sinh-Gordon物質(zhì)場獲得了標(biāo)量場的精確解,同時還得到了度規(guī)和曲率的表達(dá)式,這些解描述了時空帶上的裸奇點(diǎn),另外還導(dǎo)出了2維dilaton引力模型中的帶電sine-Gordon孤子解;第三章研究了具有弦耦合的Katanaev-Volovich引力模型中場方程的可解性質(zhì),根據(jù)標(biāo)量場的非線性微分方程的數(shù)值解,可以得到度規(guī)在原點(diǎn)外具有奇異性質(zhì),還討論了弦耦合對時空中粒子運(yùn)動速度的影響;第四章研究了2維聲學(xué)黑洞與1維流體的對應(yīng)關(guān)系,導(dǎo)出了聲學(xué)度規(guī)的表達(dá)式,證明了黑洞度規(guī)可以變?yōu)槁晫W(xué)度規(guī),推導(dǎo)了1維流體中的能量密度、速度和驅(qū)動勢,并討論了這些物理量隨空間坐標(biāo)的變化關(guān)系。本論文中具有創(chuàng)新性的工作如下:1、獲得了2維引力模型中的裸奇點(diǎn)解和帶電sine-Gordon孤子解。2、研究了弦耦合的2維引力模型中的反黑洞解,還分析了弦耦合對時空中粒子運(yùn)動速度的影響。3、研究了2維聲學(xué)黑洞與1維流體的對應(yīng)關(guān)系,獲得了能量密度、速度和驅(qū)動勢的表達(dá)式,討論了這些物理量在空間中的變化規(guī)律。
[Abstract]:In this paper, the physical properties of black holes in two-dimensional gravity and string model are studied. In the first chapter, the development and background of two-dimensional gravity and string model are introduced. In chapter 2, the solvability of the field equation of Jackiw-Teitelboim model is analyzed. The exact solution of the scalar field is obtained by introducing the Sinh-Gordon material field. At the same time, the expressions of metric and curvature are obtained. These solutions describe the bare singularities in the space-time band. In addition, the charged sine-Gordon soliton solutions in the 2-D dilaton gravitational model are derived. In chapter 3, the solvability of the field equation of Katanaev-Volovich gravity model with chord coupling is studied. According to the numerical solution of nonlinear differential equation of scalar field, the singular property of metric outside the origin can be obtained. The effect of string coupling on particle velocity in space-time is also discussed. In chapter 4, we study the corresponding relation between two-dimensional acoustical black hole and 1-dimensional fluid, derive the expression of acoustical metric, prove that black hole metric can be changed into acoustical metric, and deduce the energy density, velocity and driving potential of one-dimensional fluid. The relationship between these physical quantities and the spatial coordinates is discussed. The innovative work in this thesis is as follows: 1. The bare singularity solution and charged sine-Gordon soliton solution in the 2-D gravitational model are obtained. 2. The anti-black hole solution in the 2-D gravity model with string coupling is studied. The effect of string coupling on the velocity of particles in space-time is also analyzed. 3. The corresponding relation between the two-dimensional acoustic black hole and the one-dimensional fluid is studied, and the expressions of energy density, velocity and driving potential are obtained. The variation law of these physical quantities in space is discussed.
【學(xué)位授予單位】：四川師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：P145.8

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