2维引力与弦模型中黑洞物理性质的研究
发布时间：2018-11-05 11:42
【摘要】：本文研究了2维引力与弦模型中黑洞的物理性质,第一章介绍了2维引力与弦模型的发展状况和背景知识;第二章分析了Jackiw-Teitelboim模型中场方程的可解性质,通过引入Sinh-Gordon物质场获得了标量场的精确解,同时还得到了度规和曲率的表达式,这些解描述了时空带上的裸奇点,另外还导出了2维dilaton引力模型中的带电sine-Gordon孤子解;第三章研究了具有弦耦合的Katanaev-Volovich引力模型中场方程的可解性质,根据标量场的非线性微分方程的数值解,可以得到度规在原点外具有奇异性质,还讨论了弦耦合对时空中粒子运动速度的影响;第四章研究了2维声学黑洞与1维流体的对应关系,导出了声学度规的表达式,证明了黑洞度规可以变为声学度规,推导了1维流体中的能量密度、速度和驱动势,并讨论了这些物理量随空间坐标的变化关系。本论文中具有创新性的工作如下:1、获得了2维引力模型中的裸奇点解和带电sine-Gordon孤子解。2、研究了弦耦合的2维引力模型中的反黑洞解,还分析了弦耦合对时空中粒子运动速度的影响。3、研究了2维声学黑洞与1维流体的对应关系,获得了能量密度、速度和驱动势的表达式,讨论了这些物理量在空间中的变化规律。
[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.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：P145.8
本文编号：2311982
[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.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：P145.8
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