Momentum and velocity-dependent spacetime geometries: Traces of quantum gravity, fields in media and the gravitational field of kinetic gases

动量和速度相关的时空几何：量子引力的痕迹、介质中的场和运动气体的引力场

• 批准号: 420243324
• 负责人: Dr. Christian Pfeifer
• 金额: --
• 依托单位: Zentrum für angewandte Raumfahrttechnologie und Mikrogravitation (ZARM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/420243324?language=en
• 关键词: Momentum; velocity; dependent; spacetime; geometries

Despite all of its successes, general relativity cannot be the final answer to our understanding of gravity. On the observational side, its predictions are not consistent with the accelerated expansion of the universe and the rotation curves of galaxies. These led to the conclusion that the universe is filled with dark energy and dark matter, and only a small part is made out of the constituents of the standard model of particle physics. On the theoretical side, general relativity can still not be extended to a quantum theory of gravity in a self consistent way and moreover, it predicts singularities. Due to the absence of a fundamental theory of quantum gravity, I will employ momentum-dependent spacetime geometry as an effective model, which realises the following intuitive picture: Elementary particles, such as photons and neutrinos, probe the structure of spacetime, i.e. gravity, at scales inversely proportional to their energy. Thus, higher energetic particles interact more strongly with the quantum nature of gravity than lower energetic ones. A fundamental theory of quantum gravity should describe this effect in terms of the scattering matrices between the probe particles and gravitons. The aim is, on the one hand, to predict qualitatively and quantitatively observable effects, like energy-dependent (1) time of arrivals of photons, (2) black hole shadows, (3) gravitational lensing images as well as (4) products of particle collisions near black holes, and to identify them in data taken from telescopes like HESS, Veritas, MAGIC or the EHT. On the other hand, the mathematical relation between momentum-dependent spacetime geometry and curved non-commutative spacetimes will be investigated and extensions of the Einstein equations, which determine the momentum-dependent spacetime geometry, will be derived. An additional application of momentum-dependent spacetime geometry is the effective description of classical and quantum fields in media. A new approach to understand dark energy and dark matter is to consider physical systems in the universe which are usually modelled as fluids (the universe as a whole, ordinary and neutron stars, accretion discs) as kinetic gases. The advantage of this viewpoint is that the gravitational field of the gas can be described by a velocity-dependent Finsler spacetime geometry, which includes the contribution of the kinetic energy and the velocity distribution of the gas particles. Usually, in the Einstein-Vlasov equations, only the average over the velocity distribution of the gas particles is taken into account. This procedure enables us to construct a cosmological model which incorporates that the constituents of the cosmological fluid/gas have a velocity distribution, they move relatively to each and only propagate in the cosmological time direction on average. This may be the source of dark matter.

尽管广义相对论取得了所有成功，但它并不能成为我们理解引力的最终答案。在观测方面，其预测与宇宙的加速膨胀和星系的旋转曲线并不一致。由此得出的结论是，宇宙充满了暗能量和暗物质，只有一小部分是由粒子物理标准模型的成分组成的。在理论方面，广义相对论仍然不能以自洽的方式推广到量子引力论，而且它还预言了奇点。由于缺乏量子引力的基本理论，我将采用动量相关的时空几何作为有效模型，它实现了以下直观的画面：基本粒子，例如光子和中微子，探测时空的结构，即引力，在与它们的能量成反比的尺度上。因此，高能粒子比较低能粒子与引力量子性质的相互作用更强烈。量子引力的基本理论应该用探针粒子和引力子之间的散射矩阵来描述这种效应。一方面，其目的是预测定性和定量的可观测效应，例如与能量相关的 (1) 光子到达时间、(2) 黑洞阴影、(3) 引力透镜图像以及 (4) 产品黑洞附近的粒子碰撞，并在从 HESS、Veritas、MAGIC 或 EHT 等望远镜获取的数据中识别它们。另一方面，将研究动量相关时空几何与弯曲非交换时空之间的数学关系，并导出确定动量相关时空几何的爱因斯坦方程的扩展。动量相关时空几何的另一个应用是有效描述介质中的经典场和量子场。理解暗能量和暗物质的一种新方法是将宇宙中的物理系统视为动力学气体，这些物理系统通常被建模为流体（整个宇宙、普通星和中子星、吸积盘）。这种观点的优点是气体的引力场可以用速度相关的芬斯勒时空几何来描述，其中包括气体粒子的动能和速度分布的贡献。通常，在爱因斯坦-弗拉索夫方程中，仅考虑气体粒子速度分布的平均值。这个过程使我们能够构建一个宇宙学模型，其中包含宇宙学流体/气体的成分具有速度分布，它们相对于彼此移动并且平均仅在宇宙学时间方向上传播。这可能是暗物质的来源。