Lorentz invariance and diffeomorphism invariance in modified gravity

修正引力中的洛伦兹不变性和微分同胚不变性

• 批准号: 2249060
• 金额: --
• 依托单位: University College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2249060
• 关键词: Lorentz; invariance; diffeomorphism; modified; gravity

Research Area: Mathematical PhysicsA large number of modified theories of gravity has been proposed and studied in the last decade. Amongst those are modified teleparallel gravity models. In a suitable limit these theories become equivalent to Einstein's theory of General Relativity (GR) in which case one speaks of the teleparallel equivalent of general relativity (TEGR). While GR is, by construction, invariant under local Lorentz transformations, TEGR is only quasi-invariant in the sense that its action is locally Lorentz invariant only up to a boundary term. This does not affect the field equations of the theory which are equivalent to those of GR.This project aims to develop an in depth understanding of the role of local Lorentz transformations and local coordinate transformations in the context of modified gravity models.In the first 6-12 months the student will study various modified theories of gravity. These will contain models which are not locally Lorentz invariant or not invariant under coordinate transformations.In year 2 the student will derive the equations of motion for some of these theories and for models not previously studied. An important milestone will be to show that these equations reduce to previously studied models in a certain limit.Next, these equations will be studied in the context of spherical symmetry and in cosmology. The student will work on constructing some explicit solutions to these equations and their properties will be investigated.This investigation leads to the following interesting questions the student can study: First, the existence of regular cosmological models where the initial singularity is removed. Second, the existence of regular black hole solution.

研究领域：数学物理学在过去的十年里，人们提出并研究了大量改进的引力理论。其中包括修改后的远程平行重力模型。在适当的限度内，这些理论变得等同于爱因斯坦的广义相对论(GR)，在这种情况下，人们谈到广义相对论的远程平行(TEGR)。虽然GR在构造上是局部Lorentz变换下的不变的，而TEGR只是在其作用直到边界项的局部Lorentz不变的意义上是准不变的。这并不影响理论中与GR等价的场方程。本项目旨在深入理解局部洛伦兹变换和局部坐标变换在修正重力模型中的作用。在最初的6-12个月中，学生将学习各种修正的重力理论。这些包含的模型不是局部洛伦兹不变的，或者在坐标变换下不是不变的。在第二年，学生将为这些理论中的一些和以前没有研究过的模型推导出运动方程。一个重要的里程碑将是证明这些方程在一定的范围内归结为以前研究的模型。接下来，这些方程将在球对称和宇宙学的背景下进行研究。学生将致力于构造这些方程的显式解，并研究它们的性质。这项调查导致了学生可以学习的下列有趣的问题：第一，规则宇宙模型的存在，其中初始奇点被去除。第二，正则黑洞解的存在性。